Probability models

This chapter provides a brief introduction to some important probability models. It starts from the basic concept of probability space and random variables, cumulative distribution function, probability density function/probability mass function, moment generating function and characteristic function, followed by selected frequently-used distribution types with illustration of their applications in practical engineering. The joint probabilistic behaviour of different random variables is also discussed, including the use of copula function to construct the joint distribution functions of dependent random variables

Genetic structure analysis of Eufriesea violacea (Hymenoptera, Apidae) populations from southern Brazilian Atlantic rainforest remnants

Random amplified polymorphic DNA (RAPD) markers were used to analyze the genetic structure of Eufriesea violacea populations in three fragments (85.47, 832.58 and 2800 ha) of Atlantic rainforest located in the north of the Brazilian state of Paraná. A total of twelve primers produced 206 loci, of which 129 were polymorphic (95% criterion). The proportions of polymorphic loci in each population ranged from 57.28% to 59.2%, revealing very similar levels of genetic variability in the groups of bees from each fragment. Unbiased genetic distances between groups ranged from 0.0171 to 0.0284, the smallest genetic distance occurring between bees from the two larger fragments. These results suggest that the E. violacea populations from the three fragments have maintained themselves genetically similar to native populations of this species originally present in northern Paraná

Identification of two new mutations in the GPR98 and the PDE6B genes segregating in a Tunisian family

Autosomal recessive retinitis pigmentosa (ARRP) is a genetically heterogeneous disorder. ARRP could be associated with extraocular manifestations that define specific syndromes such as Usher syndrome (USH) characterized by retinal degeneration and congenital hearing loss (HL). The USH type II (USH2) associates RP and mild-to-moderate HL with preserved vestibular function. At least three genes USH2A, the very large G-protein-coupled receptor, GPR98, and DFNB31 are responsible for USH2 syndrome. Here, we report on the segregation of non-syndromic ARRP and USH2 syndrome in a consanguineous Tunisian family, which was previously used to define USH2B locus. With regard to the co-occurrence of these two different pathologies, clinical and genetic reanalysis of the extended family showed (i) phenotypic heterogeneity within USH2 patients and (ii) excluded linkage to USH2B locus. Indeed, linkage analysis disclosed the cosegregation of the USH2 phenotype with the USH2C locus markers, D5S428 and D5S618, whereas the ARRP perfectly segregates with PDE6B flanking markers D4S3360 and D4S2930. Molecular analysis revealed two new missense mutations, p.Y6044C and p.W807R, occurring in GPR98 and PDE6B genes, respectively. In conclusion, our results show that the USH2B locus at chromosome 3p23–24.2 does not exist, and we therefore withdraw this locus designation. The combination of molecular findings for GPR98 and PDE6B genes enable us to explain the phenotypic heterogeneity and particularly the severe ocular affection first observed in one USH2 patient. This report presents an illustration of how consanguinity could increase familial clustering of multiple hereditary diseases within the same family