We show that the top Lyapunov exponent LE(p) associated with a random product of quasi-periodic cocycles depends real analytically on the transition probabilities p whenever LE(p) is simple. Moreover if the spectrum at p is simple (all Lyapunov exponents having multiplicity one ) then all Lyapunov exponents depend real analytically on p.Universidad de Costa Rica/[]/UCR/Costa RicaFundação de Amparo à Pesquisa do Estado de São Paulo/[#18/07797-5]/FAPESP/BrasilUCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Básicas::Centro de Investigaciones en Matemáticas Puras y Aplicadas (CIMPA
