In an area, the number of days during a season when you can watch shooting (falling) stars is a Poisson r.v. with a parameter λ. The number of falling stars on each of such days is also a Poison r.v. with a parameter μ. The numbers of stars on different days are independent, and do not depend on the number of the days with falling stars.

(a) Find the expected value of the total number of stars that can be watched during the season.

(b) Find the variance of the same r.v.

(c) Show that the distribution of the total number of stars is not Poisson. (Sometimes, the distribution in hand is called Poisson-Poisson.)