Problem 1. Suppose that you arrive at the single-clerk post office to send a package and find one customer being helped and another 4 customers waiting in line. You join the end of the line. If the service times are all exponential with rate μ, what is the expected amount of time you will spend at the post office (assume customers are helped one at a time, and you will leave the post office as soon as your package is sent)?
Problem 2. Dr. Turner is reviewing her patient notes from the visits she had today. However, she is on-call and will receive pages that require immediate attention. Pages come at a Poisson rate of four pages per hour. What is the probability that in 30 minutes, Dr. Turner will receive at least 1 page?