  We show that the top Lyapunov exponent $\lambda_+(p)$ , $p = (p_1, \cdots,
p_N)$ with $p_i >0$ for each $i$, associated with a random product of
quasi-periodic cocycles depends real analytically on the transition
probabilities $p$ whenever $\lambda_+(p)$ is simple. Moreover if the spectrum
at $p$ is simple (all Lyapunov exponents having multiplicity one ) then all
Lyapunov exponents depend real analytically on $p$.
