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...

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