Tom shops for probability books forK hours, whereK is a random variable that is equally likely to be 1,2,3,or 4. The number of books N that he buys is random and depends on how long he shops according to the conditional PMF pNjK(njk) = 1 K, for n = 1; :::; k.
(a) Find the joint PMF of K and N.
(b) Find the marginal PMF of N.
(c) Find the conditional PMF of K given that N = 2.
(d) Find the conditional mean and variance of K, given that he bought at least 2 but no more than 3 books.
(e) The cost of each book is a random variable with mean 30. What is the expected value of his total expenditure?