Calls arrive to an operator at a call center at times that form a Poisson process N(t) with rate λ. The time τ devoted to a typical call has an exponential distribution with rate μ, and it is...

Calls arrive to an operator at a call center at times that form a Poisson process N(t) with rate λ. The time τ devoted to a typical call has an exponential distribution with rate μ, and it is independent of N. Then N(τ) is the number of calls that arrive while the operator is busy answering a call. Find the Laplace transform and variance of N(τ). Find P{N(τ) ≤ 1}.