A node in a communication network receives data packets of variable length. Each packet has a random number of bits that is uniformly distributed over the integers {100, 101, 102… 999}. The number of packet arrivals per minute is a Poisson random variable with a mean of 50.
(a) What is the average number of data bits per minute arriving at the node?
(b) What is the variance of the number of data bits per minute arriving at the node?