Deposits to a bank account occur at times that form a Poisson process with rate λ and the amounts deposited are independent random variables with distribution F (independent of the times). Also,...

Deposits to a bank account occur at times that form a Poisson process with rate λ and the amounts deposited are independent random variables with distribution F (independent of the times). Also, withdrawals occur at times that form a Poisson process with rate μ and the amounts deposited are independent random variables with distribution G (independent of the times). The deposits and withdrawals are independent. Let X(t) denote the balance of the bank account at time t; the balance may be negative. Find the mean, variance and distribution of X(t) when X(0) = 0.