Almae Matris Studiorum Campus

Figini, Paolo

Lecture 14 – Internatonal EconomicsNatonal Accountng and the Balance o  PaymentsPreview• The main aggregates in Natonal Accountng• Defnitons• Natonal Accountng in an Open Economy• The Current Account• The Capital Account• The Balance of Payments Account• Surplus, Defcit and Ofcial ReservesDefnitons• Gross Domestc Product (GDP): The value of all fnal goods and services produced by an economy in a given period of tme● Only fnal goods are considered to avoid double countng.● It is a fow (not a stock) variable.• Gross Natonal Product (GNP): The value of all fnal goods and services produced by the economy’s factors of producton in a given period of tme• The GNP considers the value produced by natonal factors, even if located abroad• The GDP considers the value produced within the economy, even if the factors of producton are owned by foreigners• GDP – GNP = Net Factor Payments • Usually, there are small diferences between GDP and GNPDefnitons ())• Net Natonal Product (NNP) = GNP – Depreciaton of the capital over the tme period• Nominal Value (of GDP, GNP…): it measures the value of goods and services at current prices. It does account for infaton• Real Value (of GDP, GNP…): it measures the value of goods and services at constant prices, so considering the prices of a reference year.• Real GDP = Nominal GDP  - Infaton• Infaton is measured through the CPI (Consumer Price Index) and / or GDP defator (more relevant for the producton process)• Basic identty of the Natonal Accountng:● Natonal Product = Natonal Income (if you want, S = D)Natonal Accountng in an open economy• Economic agents:● Private sector (households and frms)● Public sector (public administraton and central bank)● Foreign sector (exporters and importers)• GNP = Y = C + I + G + X – M• If we defne S = Y – C – G → S = I + (X – M)• If we distnguish public (T – G) and private sector savings• Spr = Y – T – C • Spu = T – G ● → Spr = I + (X – M) + (G - T)• Where (G – T) is government budget defcit• We already know the debate about the GDP as a proxy of welfare 6The twin defcit• (Y – T) – C – I = (G – T) + (X – M) • Spr – I = (G – T) + (X – M)• If Spr = I and (G – T) increases, then (X – M) has to become very negatve → phenomenon of twin defcits (joint presence of public defcit and trade defcit.• US as the typical caseThe Balance o  Payments Accountng• Trade Balance: the diference between the value of exports and imports of goods and services●  X – M●  X = X(world demand); M = M(Y)• Current Account: Trade Balance + Factor Income Payment• Financial Account: it takes into consideraton transactons involving sales of assets to foreigners (capital infow) or purchases of assets from foreigners (capital outlow): it is FDI + foreign portolio investments.• Balance o  Payments Account:  BOP = (X – M) + FI + FA• Diference between Account and Balance● Principle of double-entry bookkeeping → BOP = 0● Balance o  Payments (ofcial setlements balance) BOP = ORT● Ofcial Reserve Transacton = Sales or purchase of internatonal reserves (foreign assets held by the Central Bank) A quick descripton o  the BOP• Current Account: it records every transacton between the economy and the rest of the world:– Goods (cars, smartphones, toasters...)– Services (tourism, insurance, legal expenditures,..)– Income payments (profts, remitances)– Unilateral transfers (gifs)• Capital Account: small secton recording transacton of non fnancial capital assets (a patent, foreign debt forgiveness,..)• Financial Account: it records fnancial transactons (fnancial assets, FDI, currencies and variaton of ofcial reserves).• Statstcal discrepanciesAn example: the BOP  or Italy

Lecture 13 - National Accounting and the Balance of Payments

Internatinal EcinimicsLecture 05 - The Standard Trade MidelIntriductin• Standard trade midel: it is a general model that includes Ricardian (one factor of producton, diferent technologies) and Heckscher-Ohlin (two factors, diferent endowment of resources) models as special cases.• Similar features of the two models:– Diferences in labor services, labor skills, physical capital, land, and technology between countries cause diferences in producton possibility fronters, thus giving rise to trade.– A country’s PPF determines its relatve supply functin.– Natonal relatve supply functons determine the world relatve supply functon which, along with world relatve demand, determines the equilibrium under internatinal trade.Preview• We consider a model with two goods (C=clothes, F=food) and two countries (Home and Foreign)• Countries generally difer with respect to technologies and endowment of resources• The model is built on four key issues:– The relatonship between PPF and the relatve supply curve.– The relatonship between relatve prices and relatve demand.– The determinaton of world equilibrium world through RS and RD– The efect of the terms of trade on welfare• Efect of growth, tarifs, subsidies and lending on the equilibriumPriductin Pissibilites and Relatve Supply• What a country produces depends on the relatve price of C to F PC /PF.• The PPF is the one already defned in the Hecksher-Ohlin model• An economy chooses its producton of cloth QC and food QF to maximize the value if its iutput V = PCQC + PF QF, given the prices of cloth and food.– The slope of the isivalue line equals – (PC /PF)– Produce at point where PPF is tangent ti the isivalue line.• An increase in the price of cloth relatve to food PC /PF makes the isovalue line steeper.– Producton shifs from point Q1 to point Q2.– Supply of cloth relatve to food QC /QF rises.– Relatve supply if clith ti fiid increases with the relatve price if clith ti fiid.Relatve Prices Determine the Ecinimy’s OutputHiw an Increase in the RelatvePrice if Clith Afects Relatve SupplyRelatve Prices and Demand• The value of the economy’s consumpton must equal the value of the economy’s producton: PC DC + PF DF = PC QC + PF QF = V• Assume that the economy’s consumpton decisions may be represented as if they were based on the tastes of a single representatve consumer.• An indiference curve represents combinatons of cloth and food that leave the consumer equally well of (indiferent).– They are diwnward sliping – if you have less cloth, then you must have more food to be equally satsfed.– The farther they lie from the origin the more satsfed the consumers are – they prefer having more of both goods.– They becime fater when they move to the right – with more cloth and less food, an extra unit of cloth becomes less valuable in terms of how many units of food you are willing to give up for it.• In an open economy, the diference between producton and demand identfes exports and imports for the two goods.Priductin, Cinsumptin, and Tradein the Standard MidelRelatve Prices and Demand (2)• An increase in PC /PF – Shifs producton choice from from point Q1 to point Q2 and increases relatve supply fro cloth  QC /QF– Shifs consumpton choice from point D1 to point D2 (income and substtuton efect) and reduces relatve demand for cloth DC /DF.• It makes an economy that exports cloth beter if.– The isovalue line becomes steeper and a higher indiference curve can be reached.– More units of food can be imported for every unit of cloth exported.• If the economy cannot trade: –  PC /PF is determined by the intersecton of relatve demand and relatve supply for that country.– Consume and produce at point D3 where the indiference curve is tangent to the producton possibilites fronter.Efects if a Rise in the Relatve Price if Clith and Gains frim TradeDetermining Relatve Prices and the welfare efects• To determine PC /PF, use relatve supply and relatve demand.– World supply of cloth relatve to food at each relatve price (typical upward sloping shape).– World demand for cloth relatve to food at each relatve price (typical downward sloping shape).– World quanttes are the sum of quanttes from the two countries in the world: (QC + QC*)/(QF + QF*) and (DC + DC*)/(DF + DF*).• The terms if trade is the price of exports relatve to the price of imports.– When a country exports cloth (as for Home) and PC /PF increases, the terms of trade rise (they fall for Foreign, PF /PC)– Because a higher relatve price for exports means that the country can aford to buy more imports, an increase in the terms if trade increases a ciuntry’s welfare.– A decline in the terms of trade decreases a country’s welfare.Equilibrium Relatve Price with TradeEquilibrium Trade FliwsThe Efects if Ecinimic Griwth• Is economic growth in China good for the standard of living in the U.S. or in Europe? Is growth in a country more or less “valuable” when it is integrated in the world economy?• The standard trade model gives us precise answers to these questons.• Growth can stem from increases in the available resources or in more efciency in their use (innovaton).• Growth is usually biased: it occurs in one sector more than in others, causing relatve supply to change.– Rapid growth has occurred in U.S. computer industries but relatvely litle growth has occurred in U.S. textle industries.– In the Ricardian midel, technological progress in one sector causes biased growth.– In the Heckscher-Ohlin midel, an increase in one factor of producton (investment, educaton...) causes biased growth.Biased GriwthThe Efects if Ecinimic Griwth (2)• Biased growth and the resultng change in relatve supply causes a change in the terms if trade.– Biased growth in C industry (in either Hime ir Fireign) will lower PC /PF and will lower the terms of trade for C exporters.– Biased growth in F industry (in either Hime ir Fireign) will raise PC /PF and raise the terms of trade for C exporters.• Expirt-biased griwth is growth that expands a country’s producton possibilites disproportonately in that country’s export sector.– Export-biased growth tends to worsen the “growing” country’s terms of trade, to the beneft of the other country.• Impirt-biased griwth is growth that expands a country’s producton possibilites disproportonately in that country’s import sector.– Import-biased growth tends to improve the growing country’s terms of trade to the expenses of the other country.• Immiserizing griwth: a controversial issue for developing countries.Clith- and Fiid-Biased Griwth and Wirld Relatve SupplyImpirt Tarifs and Expirt Subsidies: Simultaneius Shifs in RS and RD• Impirt tarifs are taxes levied on imports.• Expirt subsidies are payments given to domestc producers that export.– Both policies infuence the terms of trade and therefore natonal welfare, although they are ofen implemented for other reasons (income distributon, industrial policy, BoP efect).• Import tarifs and export subsidies drive a wedge between (external) prices in world markets and (internal) prices in domestc markets.• Terms if trade (how much import a country can buy with one unit of export) are determined by external prices, not by internal prices, which are the ones afected by the trade policy).Relatve Price and Supply Efects if a Tarif• If Home imposes a tarif on food imports, the price of food relatve to the price of cloth rises for domestc consumers.– Domestc producers receive a lower relatve price of C, and will be more willing to switch to F producton: relatve supply if C decreases.– Domestc consumers pay a lower relatve price for C, and will be more willing to switch to C consumpton: relatve demand fir C increases.• When Home imposes an import tarif, the world terms of trade increase and the welfare if the ciuntry may increase.• The magnitude of this efect depends on the size of Home relatve to the world economy.– If Home is a small part of the world economy, its tarif policies will not change world relatve supply and demand, neither the terms of trade.– But for large countries, a tarif may maximize natonal welfare at the expense of foreign countries.Efects if a Fiid Tarif in the Terms if TradeEfects if an Expirt Subsidy• If Home imposes a subsidy on C exports, the internal price of C relatve to the price of F rises for domestc consumers.– Domestc producers receive a higher relatve price of C when they export, and will be more willing to switch to C producton: relatve supply if C will increase.– Domestc consumers must pay a higher relatve price of C to producers (otherwise domestc producers prefer to export C rather than selling it domestcally), and therefore will be more willing to switch to F consumpton: relatve demand fir C will decrease.• When Home imposes an export subsidy:– the wirld terms if trade decrease for Home decreases to the beneft of Foreign’s terms of trade.Efects if a Clith Subsidy in the Terms if TradeImplicatins if Terms if Trade Efects: Whi Gains and Whi Lises?• The standard trade model predicts the distributonal efects of policies.• The internatinal distributin if incime– An import tarif by H decreases F welfare, increases H welfare but...– An export subsidy by H reduces domestc welfare to the beneft of F.• The dimestc distributin if incime– The tarif changes the distributon of income: there is distorton in the incentves, although an improvement in the terms of trade.– Possibility of paradoxical efects: the Metzler paradix.• If Foreign subsidizes the export of a good that Home exports, it reduces its price in world markets and decreases Home’s terms of trade.• If Foreign puts a tarif on an imported good that Home imports,  it reduces its price in world markets and increases its terms of trade.Summary● The terms of trade refers to the price of exports relatve to the price of imports.● Export-biased growth reduces a country’s terms of trade, reducing its welfare and increasing the welfare of foreign countries.● Import-biased growth increases a country’s terms of trade, increasing its welfare and decreasing the welfare of foreign countries.● When a country imposes an import tarif, its terms of trade increase and its welfare may increase.● When a country imposes an export subsidy, its terms of trade decrease and its welfare decreases.

Lecture 05 - The Standard Trade Model

Carfagna, Elisabetta

Eurostathttp://ec.europa.eu/eurostat Eurostat co-ordination role of statistical activities Regulation N°223/2009 on European statistics (the so-called 'Statistical Law') provides that Eurostat is the statistical authority of the Union. Like national statistical institutes at national level, Eurostat co-ordinates statistical activities at Union level and more particularly inside the Commission. At Union level, Eurostat ensures the production of European statistics according to established rules and statistical principles, notably those laid down in the European statistics Code of Practice. Eurostat coordinates the statistical activities of the institutions and bodies of the Union, in particular with a view to ensuring consistency and quality of the data and minimising reporting burden As one of the Directorates-General of the European Commission, Eurostat is headed by a Director General and a Deputy Director General. The seven Directorates responsible for different sectors of Eurostat activities are organised as below: Cooperation in the European Statistical System; international cooperation; resources Methodology; corporate statistical and IT services National accounts, prices and key Indicators Government finance statistics (GFS) and quality Sectoral and regional statistics Social statistics Global business statisticsEuropean Statistical System (ESS) European Statistical System (ESS) was built up with the objective of providingcomparable statistics at EU level The ESS functions as a network in which Eurostat's role is fundamental to lead the wayin the harmonization of statistics in close cooperation with the national statisticalauthorities. Eurostat is responsible for development, production and dissemination of Europeanstatistics. The ESS also coordinates its work with other Commission services, agencies, the ECB(European Central Bank) and international organizations such as OECD (Organizationfor Economic Co-operation and Development), the UN, the International MonetaryFund and the World Bank. OECD https://data.oecd.org/EUROPEAN UNION STATISTICS ON INCOME AND LIVING CONDITIONS (EU-SILC) I http://ec.europa.eu/eurostat/web/microdata/european-union-statistics-on-income-and-living-conditions The European Union Statistics on Income and Living Conditions (EU-SILC) is an instrument aiming at collecting timely and comparablecross-sectional and longitudinal multidimensional microdata onincome, poverty, social exclusion and living conditions. Thisinstrument is anchored in the European Statistical System (ESS).The EU-SILC project was launched in 2003 on the basis of a"gentlemen's agreement" in six Member States (Belgium, Denmark,Greece, Ireland, Luxembourg and Austria) and Norway. The startof the EU-SILC instrument was in 2004 for the EU-15 (exceptGermany, the Netherlands, the United Kingdom) and Estonia,Norway and Iceland.EUROPEAN UNION STATISTICS ON INCOME AND LIVING CONDITIONS (EU-SILC)II The EU-SILC instrument provides two types of data: Cross-sectional data pertaining to a given time or a certain time period with variables on income, poverty, social exclusion and other living conditions Longitudinal data pertaining to individual-level changes over time, observed periodically over a four-year period. Social exclusion and housing condition information is collected mainly at household level while labour, education and health information is obtained for persons aged 16 and over. The core of the instrument, income at very detailed component level, is mainly collected at personal level.EU-SILC based datahttp://ec.europa.eu/eurostat/web/income-and-living-conditions/overview The EU-SILC has been used to provide data on the structural indicators of social cohesion (at-risk-of poverty rate, S80/S20) and in the context of the two Open Methods of Coordination in the field of social inclusion and pensions. Since 2010, the outset of the Europe 2020 strategy, EU-SILC data is being used for monitoring the poverty and social inclusion in the EU. A headline poverty target on reducing by 20 million in 2020 the number of people under poverty and social exclusion has been defined based on the EU-SILC instrument. In the same political context a broader portfolio of indicators, including plenty of numerous EU-SILC based data, constitutes the Joint Assessment Framework (JAF) of the EU2020 strategy. All datasets under the Income and Living conditions (ILC) domain contain EU-SILC data.EU SILC Primary variables I EU-SILC does not rely on a common questionnaire or a survey but on the idea of a "framework". The latter defines the harmonised lists of target primary (annual) and secondary (every four years or less frequently) variables to be transmitted to Eurostat; common guidelines and procedures; common concepts (household and income) and classifications aimed at maximising comparability of the information produced.  Target population The reference population in EU-SILC includes all private households and their current members residing in the territory of the countries at the time of data collection. Persons living in collective households and in institutions are generally excluded from the target population. Some small parts of the national territory amounting to no more than 2% of the national population and the national territories listed below may be excluded from EU-SILC. All household members are surveyed, but only those aged 16 and more are interviewed.EU SILC Primary variables II The primary variables are collected every year. These variables refer either to household or to individual (for person aged 16 and more) information and are regrouped into domains: At household level, four domains are covered: (1) basic data, (2) housing, (3) material deprivation and (4) income. The personal level is regrouped into five domains: (1) basic/demographic data, (2) education, (3) health, (4) labourand (5) income.EU SILC Primary variables IIIHousehold register (list)Household data (list)Basic dataHousingMaterial deprivationIncomePersonal register (list)Basic dataChild carePersonal data (list)Basic dataEducationHealthLabourIncomeEU SILC Primary variables IV2016 module: Access to Services (list)2015 module: Social and cultural participation and Materialdeprivation (list)2014 module: Material deprivation (list)2013 module: Well-being (list)2012 module: Housing conditions (list)2011 module: Intergenerational transmission of disadvantages (list)2010 module: Intra-household sharing of resources (list)2009 module: Material deprivation (list)2008 module: Over-indebtedness and financial exclusion (list)2007 module: Housing conditions (list)2006 module: Social participation (list)2005 module: Intergenerational transmission of poverty (list)EU SILC Secondary variables V Secondary variables are collected every five years or less frequently in the so-called ad-hoc modules. They include information either at household or personal level about specific topics. Over time, several topics have been addressedREGULATION (EC) No 543/2009 OF THE EUROPEAN PARLIAMENT AND OF THE COUNCIL of 18 June 2009 concerning crop statistics Article 5 Precision requirements 1. Member States conducting sample surveys in order to obtain statistics shall take all necessary steps to ensure that Table 1 data meet the following precision requirements: the coefficient of variation of the data to be provided by 30 September of the year n + 1 shall not exceed, at national level, 3 % for the area under cultivation for each of the following groups of main crops: cereals for the production of grain (including seed), dried pulses and protein crops for the production of grain (including seed and mixtures of cereals and pulses), root crops, industrial crops and plants harvested green. 2. A Member State which decides to use sources of statistical information other than statistical surveys shall ensure that information obtained from such sources is of at least equal quality to information obtained from statistical surveys. 3. A Member State which decides to use an administrative source shall inform the Commission in advance and shall provide details concerning the method to be used and the quality of the data from that administrative source.Quality of statistical output is in the European Statistical System Described with five maincomponents:Relevance;Accuracy and reliability; Timeliness and punctuality;Coherence and comparability;Accessibility and clarity

Eurostat

Brini, Andrea

Teoria della misura ed id integrazione

Salvaterra, Carla

Topografico	  delle	  sezioni	  di	  storia	  antica	  ANTICHITÀ	  ANT.	  GEN.	  1/…	   Manualistica	  generale	  di	  antichità	  greche	  e	  romane	  Istituzioni	  pubbliche	  Studi	  sulla	  città	  ANT.	  I	  1/…	   Diritto	  e	  istituzioni	  greche	  pubbliche	  e	  private	  ANT.	  II	   Diritto	  e	  istituzioni	  romane	  1/500	   Manuali,	  testi	  di	  teoria	  generale,	  storia	  della	  giurisprudenza	  501/1000	   Fonti	  e	  studi	  su	  singoli	  autori	  1001/5000	   Diritto	  ed	  istituzioni	  pubbliche	  5001/…	   Diritto	  ed	  istituzioni	  private	  ANT.	  III	   Antichità	  militari	  e	  navali	  1/1000	   Antichità	  militari	  1001/…	   Antichità	  navali	  ANT.	  IV1/…	   Gli	  animali	  nell’antichità	  ANT.	  V	   Antichità	  private	  1/5000	   Antichità	  private	  5001/10000	   Storia	  della	  medicina	  10001/15000	   Donne	  nel	  mondo	  antico	  15001/20000	   Schiavitù	  nel	  mondo	  antico	  20001/25000	   Sessualità	  e	  omosessualità	  nel	  mondo	  antico	  ANT	  VI	  1/…	   Antichità	  agonistiche	  e	  sportive	  ANT.	  VII	  1/…	   Storia	  della	  cultura	  antica	  ANT.	  VIII	   Cambiato	  in	  REL	  ANT.	  IX	   Archeologia	  1/2000	   Manuali	  di	  scavo	  e	  tecniche	  connesse	  Archeologia	  subacquea	  Archeologia	  industriale	  Fotografia	  aerea,	  prospezione	  grafica	  Fotografia	  archeologica,	  disegno	  archeologico	  2001/3000	   Architettura,	  urbanistica,	  materiali	  e	  tecniche,	  strade,	  topografia	  3001/3500	   Manuali	  e	  saggi	  di	  storia	  dell’arte	  3501/4000	   Mosaici	  4001/4500	   Materiali	  fittili,	  lucerne	  (bolli,	  anfore)	  ceramica	  4501/…	   Saggi	  su	  aspetti	  particolari	  ANT.	  X	  1/…	   Antichità	  giudaiche,	  Diaspora	  e	  rapporti	  con	  il	  mondo	  greco	  e	  Roma	  	  CONSULTAZIONE	  	  CONS.	  ATL.	   Consultazione	  atlanti	  CONS.	  BIBL.	   Cataloghi	  di	  biblioteche,	  saggi	  bibliografici	  e	  manuali	  biblioteconomici	  CONS.	  DID.	   Didattica	  CONS.	  DIZ.	  L.	  CL.	   Dizionari	  di	  lingue	  classiche	  CONS.	  DIZ.	  L.	  CL.	  GR.	   Dizionari	  di	  lingua	  greca,	  Thesaurus	  CONS.	  DIZ.	  L.	  CL.	  LAT.	   Dizionari	  di	  lingua	  latina,	  Thesaurus	  CONS.	  DIZ.	  L.	  MOD.	   Dizionari	  di	  lingue	  moderne	  CONS.	  ENC.	   Opere	  enciclopediche	  e	  carattere	  generale	  e	  contenuto	  specifico	  CONS.	  ENC.	  1/…	   Dizionari	  archeologici	  e	  vari	  CONS.	  GRAMM.	   Grammatiche	  CONS.	  INF.	   Consultazione	  manuali	  di	  informatica	  CONS.	  STAT.	   Opere	  di	  contenuto	  statistico:	  annuari,	  repertori	  demografici…	  CONS.	  I	   	  1/100	   Generalia	  101/200	   Nouvelle	  Clio	  201/300	   Collection	  U2	  301/400	   Marzorati	  CONS.	  II	   Introduzione	  allo	  studio	  della	  storia	  antica	  Bibliografie	  CONS.	  III	   Opere	  di	  carattere	  enciclopedico	  CONS.	  IV	   Opere	  di	  consultazione:	  storia	  greca	  CONS.	  V	   Opere	  di	  consultazione:	  storia	  romana	  CONS.	  VI	   Pubblicazioni	  dell’Instituto	  di	  Studi	  Romani	  e	  guida	  allo	  studio	  della	  civilitàa	  romana	  antica	  	  CRONOGRAFIA	  	  CRON.	  I	  1/…	   Cronografia	  	  ECONOMIA	  	  ECON.	  I	  1/…	   Testi	  di	  economia	  generale,	  economia	  agraria,	  tecnica	  bancaria	  nell’antichità,	  storia	  economica,	  problemi	  e	  lotte	  sociali	  	  EPIGRAFIA	  	  E.	  I	   Storia	  della	  scrittura	  E.	  II	   Manualistica	  1/100	   Manuali	  di	  Epigrafia	  Latina	  101/200	   Manuali	  di	  Epigrafia	  Greca	  201/…	   Studi	  su	  singoli	  problemi	  connessi	  con	  l’Epigrafia	  E.	  III	   Raccolte	  di	  epigrafi	  per	  tipo	  e	  per	  periodo	  1/100	   Epigrafi	  latine	  101/150	   Epigrafi	  greche	  e	  latine	  relative	  allo	  stesso	  soggetto	  151/200	   Tavole	  di	  concordanza	  201/…	   Epigrafi	  greche	  E.	  IV	   Raccolte	  di	  epigrafi	  e	  studi	  di	  epigrafia	  relativi	  all’Italia	  E.	  IV.	  1	   Italia	  E.	  IV.	  2	   Roma	  E.	  IV.	  3	   Singole	  località	  italiane	  E.	  V	   Raccolte	  di	  epigrafi	  e	  studi	  di	  epigrafia	  relativi	  alle	  regioni	  occidentali	  e	  danubiane	  E.	  V.	  1	   Gallie	  E.	  V.	  2	   Spagna	  E.	  V.	  3	   Britannia	  E.	  V.	  4	   Germanie	  e	  Retia	  E.	  V.	  5	   Norico,	  Pannonia,	  Illirico,	  Mesie	  E.	  V.	  6	   Dacia	  E.	  VI	   Raccolte	  di	  epigrafi	  e	  studi	  di	  epigrafia	  relativi	  a:	  Grecia,	  isole	  greche,	  Tracia	  e	  Mar	  Nero	  E.	  VI.	  1	   Grecia	  E.	  VI.	  2	   Atene	  E.	  VI.	  3	   Peloponneso	  E.	  VI.	  4	   Grecia	  centrale	  E.	  VI.	  5	   Macedonia	  E.	  VI.	  6	   Isole	  E.	  VI.	  7	   Tracia,	  Mar	  Nero	  E.	  VII	   Raccolte	  di	  epigrafi	  e	  studi	  di	  epigrafia	  relativi	  a:	  Asia,	  Siria,	  Egitto	  e	  Cirenaica	  E.	  VII.	  1	   Asia	  E.	  VII.	  2	   Bitinia,	  Ponto,	  Eolide,	  Galazia	  E.	  VII.	  3	   Ionia,	  Lidia	  E.	  VII.	  4	   Caria,	  Licia,	  Panfilia,	  Cilicia,	  Pisidia	  E.	  VII.	  5	   Frigia,	  Cappadocia,	  Licaonia,	  Armenia	  E.	  VII.	  6	   Palestina,	  Siria	  E.	  VII.	  7	   Egitto	  E.	  VII.	  8	   Cirene	  E.	  VIII	   Raccolte	  di	  epigrafie	  e	  studi	  di	  epigrafia	  relativi	  alle	  province	  africane	  E.	  VIII.	  1	  	   Africa	  E.	  VIII.	  2	   Africa	  singole	  località	  E.	  IX	   Raccolte	  epigrafiche	  per	  luogo	  di	  conservazione	  E.	  IX.	  1	   Musei	  europei	  E.	  IX.	  2	   Musei	  extraeuropei	  	  ESTRATTI	  	  ESTR.	   Estratti	  	  FONTI	  	  F.	  Be.	  Le.	  G.	  	   Classici	  greci	  ed.	  Les	  Belles	  Lettres	  F.	  Be.	  Le.	  L.	  	   Classici	  latini	  ed.	  Les	  Belles	  Lettres	  F.	  C.	  C.	  L.	   Corpus	  Christianorum,	  serie	  latina	  F.	  G.C.S.	   Die	  Griechische	  Christlichen	  Schriftsteller	  F.	  Loeb	  G.	   Classici	  greci	  ed.	  Loeb	  F.	  Loeb	  L.	   Classici	  latini	  ed.	  Loeb	  F.	  M.	  G.	  H.	   Monumenta	  Germaniae	  Historica	  F.	  Oxon.	  G.	   Classici	  greci	  ed.	  Oxoniense	  F.	  Oxon.	  L	   Classici	  latini	  ed.	  Oxoniense	  F.	  P.	  G.	   Patrologiae	  cursus	  completus.	  Omnium	  SS.	  Patrum,	  Doctorum	  Scriptorumque	  Ecclesiasticorum	  Graecorum	  F.	  P.L.	   Patrologiae	  cursus	  completus.	  Omnium	  SS.	  Patrum,	  Doctorum	  Scriptorumque	  Ecclesiasticorum	  Latinorum	  F.	  P.	  L.	  S.	   Patrologiae	  cursus	  completus,	  serie	  Latina	  Supplementa	  F.	  RACC.	  1/…	   Raccolte	  di	  fonti	  F.	  T.	   Autori	  tradotti	  senza	  testo	  a	  fronte	  F.	  Teub.	  G.	   Classici	  greci	  ed.	  Teubner	  F.	  Teub.	  L.	   Classici	  latini	  ed.	  Teubner	  F.	  Var.	  G	   Fonti	  varie:	  autori	  greci	  F.	  Var.	  G.	  H.	   Fonti	  varie:	  Jacoby:	  Die	  Fragmente	  der	  Griechischen	  Historiker	  F.	  Var.	  L.	   Fonti	  varie:	  autori	  latini	  	  ITALIA	  	  ITALIA	  I	   Studi	  generali	  Studi	  su	  aree	  greografiche	  regionali	  ITALIA	  II	   Studi	  locali:	  monumenti,	  musei,	  ville	  antiche,	  pinacoteche,	  città	  o	  luoghi	  di	  interesse	  storico,	  archeologico,	  artistico	  ITALIA	  III	   Guide:	  per	  lo	  più	  quelle	  del	  Ministero	  della	  Pubblica	  Istruzione	  III	  C.	  A.	   Carte	  archeologiche	  delle	  città	  Italiane	  a	  cura	  del	  Ministero	  della	  Pubblica	  Istruzione	  e	  altre	  ITALIA	  IV	   Forma	  Italiae	  ITALIA	  V	   Studi	  locali	  relativi	  all’Emilia	  Romagna	  	  LESSICI	  	  LESS.	   Lessici	  di	  singoli	  autori	  e	  fonti	  lessicografiche	  	  METROLOGIA	  	  METR.	   Studi	  di	  metrologia	  	  MISCELLANEE	  	  MISC.	  I	   Raccolte	  di	  scritti	  dello	  stesso	  autore	  MISC.	  II	   Scritti	  in	  onore	  o	  in	  memoria	  di	  studiosi	  MISC.	  III	   Miscellanee,	  atti	  di	  congressi,	  convegni,	  simposi,	  ecc.	  MISC.	  IV	   Serie,	  collane	  	  NARRATIVA	  	  NARR.	   Opere	  di	  narrativa	  con	  soggetti	  relativi	  al	  mondo	  antico	  	  NUMISMATICA	  	  NUM.	  I	  1/…	   Opere	  generali	  NUM.	  II	  1/…	   Numismatica	  greca:	  opere	  generali	  NUM.	  III	   Numismatica	  greca	  1/1000	   Studi	  particolari	  1001/1500	   Monetazione	  provinciale	  1501/…	   Monetazione	  celtica	  e	  iberica	  NUM.	  IV	  1/…	   Numismatica	  romana:	  opere	  generali	  NUM.	  V	  1/…	   Numismatica	  romana:	  studi	  particulari	  NUM.	  VI	  1/…	   Varie	  NUM.	  VII	  1/…	   Rinvenimenti	  monetali	  	   	  	  ORIENTALISTICA	  	  OR.	  CONS.	   Opere	  onnicomprensive	  ed	  enciclopediche,	  repertori	  bibliografici	  OR.	  I	   FONTI,	  EPIGRAFIA	  1/1000	   Generalia	  (inter-­‐areale)	  1001/…	   Mondo	  fenicio	  d’occidente	  1000/1200	   Generale	  e	  Nord	  Africa	  1201/1250	   Malta	  1251/1300	   Italia	  in	  generale	  1301/1400	   Sicilia	  1401/1700	   Sardegna	  1701/2000	   Spagna	  2001/3000	   Mondo	  egeo-­‐anatolico	  3001/4000	   Mondo	  siro-­‐palestinese	  4001/5000	   Mesopotamia	  pre-­‐ellenistica	  5001/6000	   Arabia	  pre-­‐islamica	  6001/7000	   Oriente	  ellenizzato	  7001/8000	   Iran	  pre-­‐islamico	  8001/9000	   Asia	  Media	  (Asia	  centrale,	  India)	  OR.	  II	   LINGUISTICA	  (LESSICI	  E	  GRAMMATICHE)	  1/1000	   Generalia	  (inter-­‐areale)	  1001/	  2000	   Mondo	  fenicio	  d’occidente	  2001/3000	   Mondo	  egeo-­‐anatolico	  3001/4000	   Mondo	  siro-­‐palestinese	  4001/5000	   Mesopotamia	  pre-­‐ellenistica	  5001/6000	   Arabia	  pre-­‐islamica	  6001/7000	   Oriente	  ellenizzato	  7001/8000	   Iran	  Pre-­‐islamico	  8001/9000	   Asia	  Media	  (Asia	  centrale,	  India)	  OR.	  III	   STORIA,	  ANTICHITA’	  1/1000	   Generalia	  (inter-­‐areale)	  1001/…	   Mondo	  fenicio	  d’occidente	  1000/1200	   Generale	  e	  Nord	  Africa	  1201/1250	   Malta	  1251/1300	   Italia	  in	  generale	  1301/1400	   Sicilia	  1401/1700	   Sardegna	  1701/2000	   Spagna	  2001/3000	   Mondo	  egeo-­‐anatolico	  3001/4000	   Mondo	  siro-­‐palestinese	  4001/5000	   Mesopotamia	  pre-­‐ellenistica	  5001/6000	   Arabia	  pre-­‐islamica	  6001/7000	   Oriente	  ellenizzato	  7001/8000	   Iran	  pre-­‐islamico	  8001/9000	   Asia	  Media	  (Asia	  centrale,	  India)	  OR.	  IV	   ARTE,	  ARCHEOLOGIA	  1/1000	   Generalia	  (inter-­‐areale)	  1001/…	   Mondo	  fenicio	  d’occidente	  1000/1200	   Generale	  e	  Nord	  Africa	  1201/1250	   Malta	  1251/1300	   Italia	  in	  generale	  1301/1400	   Sicilia	  1401/1700	   Sardegna	  1701/2000	   Spagna	  2001/3000	   Mondo	  egeo-­‐anatolico	  3001/4000	   Mondo	  siro-­‐palestinese	  4001/5000	   Mesopotamia	  pre-­‐ellenistica	  5001/6000	   Arabia	  pre-­‐islamica	  6001/7000	   Oriente	  ellenizzato	  7001/8000	   Iran	  pre-­‐islamico	  8001/9000	   Asia	  Media	  (Asia	  centrale,	  India)	  OR.	  V	   Egitto	  1/100	   Repertori,	  bibliografie	  e	  generalia	  101/300	   Grammatiche,	  dizionari,	  lessici	  vari	  301/600	   Fonti	  geroglifiche	  (letterarie	  e	  non)	  601/800	  e	  	  2801/4000	  Storia	  e	  civilità	  801/1200	   Arte	  e	  archeologia	  1201/1500	   Demotico	  (escluse	  grammatiche	  e	  dizionari)	  1501/1800	   Copto	  (escluse	  grammatiche	  e	  dizionari)	  1801/2000	   Varie	  4001/5000	   Religione	  e	  filosofia	  8001/9000	   Storia	  dell’Egittologia	  10001/11000	   Relazioni	  di	  scavo	  11001/12000	   Cataloghi	  di	  collezioni	  OR.	  MISC.	  I	   Raccolte	  di	  scritti	  dello	  stesso	  autore	  OR.	  MISC.	  II	   Scritti	  in	  onore	  o	  in	  memoria	  di	  studiosi	  OR.	  MISC.	  III	   Atti	  di	  convegni,	  congressi	  OR.	  MISC.	  IV	   Serie,	  collane	  	  PAPIROLOGIA	  	  P	  I	   Manualistica	  generale	  di	  Papirologia	  P	  II	   Paleografia	  (storia	  della	  scrittura	  attraverso	  i	  papiri)	  P	  III	   Lessici	  P	  IV	  	   Raccolte	  di	  papiri	  P	  V	   Studi	  di	  Papirologia	  	  PERIODICI	  	  PER	   Periodici	  	  PROSOPOGRAFIA	  	  PROS.	   Prosopografia	  1/500	   Raccolte	  di	  nomi	  di	  personaggi	  storici;	  elenchi	  e	  studi	  su	  persone	  (magistrati,	  senatori,	  ecc.)	  che	  hanno	  un	  qualche	  interesse	  storico	  o	  che	  hanno	  rivestito	  cariche	  501/…	   Studio	  di	  titolature	  imperiali	  	   	  PROVINCE	   	  PROV.	  GEN.	  1/…	   Manualistica	  Storia	  delle	  esplorazioni	  e	  scoperte	  Geografia	  storica:	  opere	  generali	  PROV.	  I	  1/…	   Amministrazione	  provinciale	  PROV.	  II	   Province	  occidentali	  1/1000	   Generalia	  1001/2000	   Iberia	  2001/3000	   Gallie	  3001/4000	   Germanie-­‐Rezia-­‐Norico	  4001/5000	   Britannia	  5001/6000	   Altre	  province	  occidentali	  PROV.	  III	  1/…	   Province	  illiriche,	  adriatiche:	  Dalmazia,	  Epiro,	  Macedonia,	  Albania	  PROV.	  IV	   Province	  danubiane	  1/1000	   Generalia	  1001/2000	   Rezia,	  Norico,	  Pannonia	  2001/3000	   Dacia	  3001/4000	   Mesia,	  Tracia	  PROV.	  V	  1/…	   Ponto	  Eusino	  PROV.	  VI	   Acaia	  e	  province	  asiatiche	  1/1000	   Generalia	  1001/2000	   Grecia,	  Isole	  greche,	  Creta	  2001/3000	   Penisola	  anatolica,	  Rodi,	  Cipro	  3001/4000	   Siria,	  Palestina,	  Arabia	  4001/5000	   Mesopotamia,	  Regno	  partico	  PROV.	  VII	  1/…	   Egitto	  PROV.	  VIII	  1/…	   Province	  africane,	  Mauretania,	  Cirenaica,	  Libia,	  Tripolitania,	  Etiopia,	  Marmarica,	  Numidia	  PROV.	  IX	  1/…	   Guide	  (richiedere	  al	  personale)	  PROV.	  X	  1/…	   Geografia:	  tutto	  ciò	  che	  attiene	  alla	  geografia	  moderna	  (climatologia	  ecc.)	  PROV.	  XI	  1/…	   Carte	  geografiche	  (richiedere	  al	  personale)	  	  RELIGIONI	  NEL	  MONDO	  CLASSICO	  	  REL.	   Antichità	  religiose	  1/800	  	  300/…	  Saggi	  generali	  Antropologia	  religiosa	  EPRO	  800/1200	   Grecia:	  Manuali	  e	  saggi	  generali	  sulla	  religione	  greca	  1201/2000	   Grecia:	  Culti,	  riti,	  sacerdozi	  2001/2600	   Roma:	  Manuali	  e	  saggi	  generali	  sulla	  religione	  romana	  2601/3600	   Roma:	  Culti,	  riti,	  sacerdozi	  3601/3800	   Oracoli	  e	  mantica	  greca	  e	  romana	  3801/4000	   Culti	  orientali:	  feste	  e	  riti	  4001/6000	   Antichità	  cristiane	  6001/7000	   Saggi	  sui	  miti,	  lessici	  mitologici	  7001/…	   Divinazione,	  alchimia,	  astrologia,	  magia,	  aretalogia	  	   	  STORIA	  GRECA	   	  SG.	  I	  1/…	   Preistoria	  ed	  età	  micenea	  SG.	  II	  1/…	   Studi	  generali,	  manualistica	  SG.	  III	  1/10000	   L’età	  arcaica	  ed	  il	  V	  sec.	  fino	  alle	  guerre	  persiane	  comprese;	  storie	  di	  singole	  località	  10000/20000	   Il	  V	  sec.	  20000/…	   Il	  IV	  sec.	  SG.	  IV	  1/5000	   Alessandro	  Magno	  5000/…	   L’Ellenismo	  SG.	  V	  1/…	   Le	  monarchie	  ellenistiche	  SG.	  VI	  1/…	   Magna	  Grecia	  e	  Occidente	  greco	  	  STORIA	  ROMANA	  	  SR.	  I	   Studi	  generali	  Manualistica	  1/100	   Storia	  repubblicana	  101/…	   Storia	  imperiale	  SR.	  II	  1/…	   Storia	  delle	  origini	  di	  Roma	  SR.	  III	  1/…	   Etruscologia	  e	  antichità	  italiche	  SR.	  IV	   Storia	  repubblicana	  1/100	   Dalla	  caduta	  della	  Monarchia	  alle	  guerre	  puniche	  escluse	  101/…	   Dalle	  guerre	  puniche	  ai	  Gracchi	  SR.	  V	   I	  Gracchi	  ed	  il	  Principato	  1/10000	   Dai	  Gracchi	  a	  Cicerone	  10001/20000	   Da	  Cicerone	  a	  Cesare	  compreso	  20001/30000	   Problemi	  generali	  del	  passaggio	  dalla	  Repubblica	  al	  Principato	  30001/40000	   Ottaviano	  Augusto	  40001/50000	   Influenza	  dell’età	  augustea	  in	  campo	  culturale	  50001/…	   Aspetti	  ideologici	  e	  culturali	  del	  Principato	  SR.	  VI	   Storia	  imperiale	  1/100	   Manualistica	  101/1200	   Giulio	  Claudi	  e	  Flavi	  1201/2300	   Imperatori	  d’adozione	  2301/3400	   I	  Severi	  3401/4500	   La	  crisi	  del	  III	  sec.	  4501/…	   La	  tetrarchia	  SR.	  VII	   Tardo	  antico	  e	  Cristianesimo	  1/10000	   Manualistica	  generale	  sul	  Basso	  Impero	  10001/20001	   Costantino	  e	  successori	  20001/30000	   Rapporti	  fra	  Cristianesimo	  ed	  Impero	  30001/…	   Storia	  bizantina:	  Imperio	  Romano	  d’Oriente	  	  STORIA	  DEGLI	  STUDI	  	  ST.	  ST.	  1/…	   Storia	  degli	  studi	  Storia	  della	  storiografia	  moderna	  sul	  mondo	  antico	  	  STORIOGRAFIA	  	  STOR.	  I	   Studi	  generali	  di	  storiografia	  1/10300	   Problematiche	  di	  storiografia,	  metodologia	  10301/…	   Saggi	  di	  linguistica	  STOR.	  II	  1/…	   Rassegne:	  studi	  su	  singoli	  problemi	  di	  storiografia	  greca	  e	  romana	  STOR.	  III	   Autori:	  studi	  particolari,	  monografie	  su	  determinati	  autori	  o	  gruppi	  di	  essi,	  commentari	  	  TECNOLOGIA	  	  TECN.	  I	  1/…	   Opere	  generali	  sulla	  tecnologia	  nell’Antichità	  	  TRADIZIONE	  DELL’ANTICHITÀ	  	  TRAD.	  ANT.	   Tradizione	  dell’Antichità:	  Studi	  e	  revisioni	  critiche	  di	  autori	  che	  hanno	  tramandato	  testi	  antiquari	  ed	  epigrafici;	  studi	  sull’influenza	  della	  storia	  antica	  nella	  cultura	  moderna	  	  

origanizzazione biblioteca

Ferrari, Federica

    The LANGUAGE of  PERSUASION in POLITICS (50 minutes)  1. How did Aristotle define rhetoric? ……………………………………………………………. ……………………………………………………………………………………………………. How did Plato define rhetoric? …………………………………………………………………… ……………………………………………………………………………………………………..  2. What are the denotation and the connotation of the word spin-doctor? Denotation: someone who…………………………………………………….. Connotation: …………………………………………………………………..  3. Give an example of textual evaluation …………………………………………………………  4. What kind of evaluation is exemplified by President Bush’s statement: “Forty-one per cent of those 10 million [people who voted in the first Afghan elections] are women”? …..………………... …………………………………………………………………………………………………………  5. What is an insider word?.............................................................................................................  Give three examples of insider words from politics ………………………………………………. ………………………………………………………………………………………………………  6. Do incumbent parties generally use positive or  negative campaigning? Explain why …………………………………………………………………………………………………….. ……………………………………………………………………………………………………..  7. “How can [politician X] possibly be a socialist when he is so wealthy?” is an example of which kind of argument? …………………………………………………………………………………………………….. “Let's just say that global warming deniers are now on a par with Holocaust deniers” is an example of which kind of argument? …………………………………………………………………………………………….  8. From the Declaration of Independence:  He is at this time transporting large armies of foreign mercenaries to compleat (sic) the works of death, desolation and tyranny … scarcely paralleled in the most barbarous ages, and totally unworthy of the Head of a civilized nation.  Find the bicolon: ……………………………………………………………………………………… Find the tricolon: ……………………………………………………………………………………...  From Dr Martin Luther King’s speech I Have a Dream: ‘…the negro finds himself an exile in his own land’ is an example of which rhetorical figure? ………………………………………………  9.  What is an oxymoron? ………………………………………………………………………… Give three examples of oxymorons used in politics from the book ………………………………………………………………………………………………………. ………………………………………………………………………………………………………. ………………………………………………………………………………………………………..  10. Fill in the following table:  Metaphor       Target           Source                    Grounds of the analogy?      Evaluation The long night of captivity     Blair is Bush’s poodle1     L’azienda Italia     1 barboncino  11. Are the following excerpts anaphoric or cataphoric or do they do both?  a) Now the problem is that we’re not thinking about it in very innovative ways. (Nye) …………….  b) And by the way, mistrust was always very important for democracy. This is why you have checks and balances. (Krastev)  …………………………………………. c)  That’s cool thing number one. Cool thing number two is [. . .] (Tandon) ………………………   12. Explain the difference between an assertion and a presupposition with examples of each …….. ………………………………………………………………………………………………………..  ……………………………………………………………………………………………………….. 13. Fill in the gaps in the following: Satire uses laughter to …………... .  It differs from simple criticism in making an …………….. attack on its object  Only individuals who possess ……………… can be satirized. Satire depends on the comparison of two worlds, one ……………... and one ……………… .  It often uses …………….. of a style of speaking or writing. Satire is not just funny but has a …………… . 14. Who was eligible to vote in the Scottish Referendum (underline the correct answer)? a) People born in and resident in Scotland?   b) People resident in Scotland? c) People born in Scotland and resident in the United Kingdom? d) People born in Scotland and resident in the European Union?  15. What is meant be ‘engendered evaluation’ and give an example from the book……………….. ………………………………………………………………………………………………………. Example: ……………………………………………………………………………………………. 

Sample esame nonografico non frequentanti

Turchetti, Giorgio

Capitolo 11

Mingione, Emanuele

1. Compute the following limitlimx→0sinx√1x2 + x.Solution: √1x2 + x=1|x|√11 + 1xSince limx→0± sin x|x| = ±1 and limx→0√11 + 1x= 0 thenlimx→0sinx√1x2 + x= limx→0sinx|x| limx→0√11 + 1x= 02. Find the solution y(t) of the Cauchy problemy′′ + 4y′ + y = 0y′(0) = 2y(0) = 0.and then compute limx→+∞ y(x).Solution: the characteristic equation isλ2 + 4λ+ 1 = 0→ λ = −2±√3Then a general solution is of the typey(x) = C1e−2+√3 + C2e−2−√3The initial conditions gives C1 = − 1√3 and C2 = 1√3 . Thenlimx→+∞ y(x) = 03. Consider the function f(x) = log(x2 + 1). Find the domain, the sign, the asymptotes, maximum andminimum points, inflection points and sketch the graph.Solution: Domain = R, Range = R+, increasing for x > 0,decreasing for x < 0 Minimum at x = 0,Inflection points x = ±14. Given the following vectors in R3: ~a = 101 , ~b = 020 and ~c = 011. Find the angles betweenall the pairs of these vectors, the area of the parallelogram spanned by ~a and ~b and the volume of theparallelepiped spanned by ~a, ~b and ~c.Solution:|~a| =√2, |~b| = 2, |~c| =√2and~a ·~b = 0, ~a · ~c = 1, ~b · ~c = 2Thencos θ(~a,~b) = 0, cos θ(~a,~c) =12√2, cos θ(~b,~c) =1√2The area A of the parallelogram spanned ~a and ~b is given by A = |~a×~b|.~a×~b =−202Then|~a×~b| = 2√(2)The volume V of the parallepiped spanned ~a, ~b and ~c is given by V = |(~a×~b) · ~c|. Now(~a×~b) · ~c =−202 ·011 = 2and then V = 2.5. Using the inverse matrix method, solve the following linear systemx− 4y = 62x+ y − z = −3x+ 2y − z = 0.Solution: x = −6, y = −3, z = −126. Find the eigenvalues and eigenvectors of the matrix A =(2 −1−2 0).Solution: Eigenvalues λ1 = 1 +√3 λ2 = 1−√3Eigenvectors~v1 = (12(−1−√(3)), 1), ~v2 = (12(−1 +√(3)), 1)7. Consider the functionf(x, y) = xy +13x3 − 2y2Compute its gradient and its Hessian matrix. Classify its critical points.Solution: The gradient of the function is∇f =(x2 + yx− 4y)while the Hessian matrixH =(2x 11 −4)The are two critical points given by∇f = ~0→ (x, y) = (0, 0)or(x, y) = (−1/4,−1/16)where (0, 0) is a saddle point while (−1/4,−1/16) is a maximum.8. Consider the functionsf(x, y) = x2 + y2 − xy , g(x, y) = x+ y − 1 .Use the method of Lagrange Multipliers to find the minimum of f subject to the constraint g(x, y) = 0.Solution: The Lagrangian function isL(x, y, λ) = x2 + y2 − xy + λ(x+ y − 1)Then∇L =2x− y + λ2y − x+ λx+ y − 1The condition ∇L = ~0 implies thatx = 1/2, y = 1/2, λ = 09. Consider a fair dice with 4 faces and roll it twice independently . Let us denote by A the event ”thefirst result is a divisor of 5” and B the event ”the sum gives 4”. Are A and B independent events?Justify your answer.Solution: the probability space is determined byΩ = {(1, 1), (1, 2), (2, 1), . . . , (4, 4)} and p(ω) = 1/16, ∀ω ∈ ΩA = {(1, 1), (1, 2), (1, 3), (1, 4)} → P (A) = 4/16 = 1/4B = {(1, 3), (3, 1), (2, 2)} → P (B) = 3/16A ∩B = {(1, 3)} → P (A ∩B) = 116the A and B are not independent events.10. Consider the probability space of the above exercise. Let X be a random variable which takes value20 if the sum of the two results is 5, −30 if the sum of the two results is 3 and 10 otherwise. Computethe expected value of X and variance of X.Solution: in general the expected value of a random variable X isE(X) =∑ω∈Ωp(ω)X(ω)Now consider the eventsA ”the sum of the two results is 5”, B ”the sum of the two results is 3” thenA = {(2, 3), (3, 2), (1, 4), (4, 1)}B = {(1, 2), (2, 1)}By definition the random variable X satisfiesX(ω) =20 ω ∈ A−30 ω ∈ B10 otherwiseand then since p(ω) = 116 for all ω ∈ Ω we have thatE(X) =116(20 · 4− 30 · 2 + 10 · 10) = 152In general the variance of a random variable X is given byV ar(X) = E(X2)− E(X)2The random variable X2 satisfiesX2(ω) =400 ω ∈ A900 ω ∈ B100 otherwiseand thenE(X2) =116(400 · 4 + 900 · 2 + 100 · 10) = 275Hence the variance isV ar(X) = 275− (15/2)2 = 875/4

Solutions, Final Exam Simulation, May 23th 2018

Giovanardi, Daniela

L'inchiesta epidemiologica della Legionellosi

Cattabriga, Alessia

12th, June 2018 Universitary badge n. . . . . . . . . . . . . . . . . . . . .Linear algebra - written testOral exam on:  June 18th morning  June 18th afternoon July 6thTotal number of sheet (handed): . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .In each exercise, write down the procedure or give explanations: a solution withoutprocedure or explanations won’t be evaluated, even if it is correct. You can do theexercises in the order you prefer: notice that it is possible to solve any of them, evenwithout having solved the previous ones.1) Consider the following linear system in the real unknowns x1, x2, x3 and de-pending on the parameter λ ∈ RS :−x1 + x2 − x3 = 1−x1 + x2 + λx3 = 1x1 − x2 = 1.(a) Find all the values of λ ∈ R, if any, for which the system admits nosolutions. (4 points)(b) Let A be the coefficient matrix of the system: is it possible to find avector d ∈ R3 such that the system Ax = d has just one solution? (2points)(c) Fix λ = 0. Find the least square solution of the system. (6 points)(d) Fix λ = −1. Write, if possible, the column of constant terms of thesystem S as a linear combination of the columns of A. (3 points)2) Consider the following matrix with real coefficientsB = 1 0 0 11 0 0 10 1 0 0 ,and let FB : R4 → R3 be the canonical linear transformation associated to B,that is the transformation defined by FB(x) = Bx.(a) Compute a minimal Cartesian representation for span{FB(1,−1, 1,−1)}.(3 point)(b) Compute a basis for the kernel of FB. (3 points)(c) Find, if possible, a vector of R3 not belonging to the range of FB. (3points)(d) Find, if possible, an endomorphism f of R3 such that imf = ker f . (2points)3) Consider the following matrix with real coefficientsC =3 1 0 00 3 0 00 0 4 00 0 1 5 .(a) Find the spectrum of the matrix. (3 points)(b) Choose an eigenspace and find a basis for its orthogonal complement. (2points)(c) Find, if possible, a diagonal matrix D and a regular matrix E such thatC = EDE−1. (2 points)

University of Bologna

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