Alvin shops for probability books for K hours, where K is a random variable that is equally likely to be 1, 2, 3, .., 5. The number of books N that he buys is random and depends on how long he shops according to the conditional PMF pN|K(n|k)=1/k, for n = 1, . . . , k.
a)Find the conditional mean and variance of K, given that he bought at least 2 but no more than 3 books.
b)The cost of each book is a random variable with mean $26. What is the expected value of his total expenditure?
