Suppose that traffic accidents occur in a certain region according to a Poisson process with rate…

Suppose that traffic accidents occur in a certain region according to a Poisson process with rate λ = 2 per day. Suppose also that the number M of persons involved in a given accident has a geometric distribution with parameter p = 1/2. That is,

(a) Calculate the mean and the variance of the number of persons involved in an accident over an arbitrary week.

(b) Let T be the random variable denoting the time between the first person and the second person involved in an accident, from the initial time. Calculate the distribution function of T