The arrival of buses carrying visitors to the Houston Livestock Show follows a Poisson process with rate . A bus carries i visitors with probability i, i = 1, 2, ... . The sojourn times of each visitor at Astrohall are independent and identically distributed (i.i.d.) random variables with a common distribution G. Assume that sojourn times are independent of the arrival process and Astrohall can accommodate all visitors who show up at the show. Let X(t) denote the number of visitors who arrive during (0, t) that are still in Astrohall at time t.

a) Find E[X(t)]

b) Does {X(t), t 0} follow a Poisson process?