Yes, but you can get other quantities with this approach as well (though not in nearly as nice a form). To do this, consider the random matrix t = Bernoulli(T)

Yes, but you can get other quantities with this approach as well (though not in nearly as nice a form). To do this, consider the random matrix t = Bernoulli(T) (i.e., T = E[t]) The distribution is m_n = M_1 t_1 ... t_n, which has expected value M_n = E[m_n] = E[M_1 t_1 ... t_n] = M_1 T^n Here, each of the t_i is an i.i.d. sample of t. You can similarly compute the variance: Var[m_n] = Var[M_1 t_1 ... t_n] I don't know a closed form for this off the top of my head, but at this point simulations are probably the best way to go.