Hello everyone. I'm stuck with this problem. I need your help...

Alvin shops for probability books for K hours, where K is a random variable that is equally likely to be 1, 2, 3, .., 7. 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.

- Find the joint PMF of K and N:

pN,K(n=4,k=5)= - pN,K(n=1,k=6)=
- Find the marjinal PMF of N:

pN(n=3)= - pN(n=4)=
- Find the conditional PMF of K given that N=6.

pK|N(k=3|6)= - pK|N(k=8|6)=
- Find the conditional mean and variance of K, given that he bought at least 2 but no more than 3 books.

Conditional mean: - Conditional variance:
- The cost of each book is a random variable with mean $22. What is the expected value of his total expenditure?

**Hint **: Condition on the events {K=1},..{K=7}, and use the total expectation theorem.

Any answers appreciated...