The number of people who enter a pizzeria in a period of 15 minutes is a non-negative random variableKwith known moment gener- ating functionMK(t) =E(etK). Each person who comes in buys a pizza. There arentypes of pizzas, and each person is equally likely to choose any type of pizza, independently of what anyone else chooses.

Give a formula, in terms ofMK(.), for the expected number of all the different types of pizzas ordered.

(c) (20 marks) The number of people who enter a pizzeria in a period of 15 minutes is a non-negative random variable K with known moment gener- ating function M K(t) = E(etK). Each person who comes in buys a pizza. There are n types of pizzas, and each person is equally likely to choose any type of pizza, independently of what anyone else chooses. Give a formula, in terms of M K(.), for the expected number of all the different types of pizzas ordered