Thread: Maths problem

The number of phone calls received at a certain residence in any period of t hours is a Poisson
random variable with parameter lambda = ut for some u > 0. What is the probability that no calls are
received during a period of t hours? Denoting by T the time (in hours) at which the rst call after
time zero is received, write down an expression for Pr(T < t). What is the name of the distribution
of the random variable T?

Can anyone help with this problem?

Hey wrexlive1.

Hint: Do you know the waiting time distribution between successive events (Hint: Look at the exponential distribution or at waiting times in your notes).