I am looking for help in solving the following problem. Although it looks like a homework problem it's not, it's just a practice in preparation for my exam:
We consider an $M/M/\infty$ where the arrival rate is $\lambda$ and service rate is $\mu$. In addition suppose each customer receives a reward upon departing the queue. Suppose the rewards are iid Exponential($\gamma$). Find the expected value and variance of the total reward paid by time 25.