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.

  1. Find the joint PMF of K and N:
  2. pN,K(n=1,k=6)=
  3. Find the marjinal PMF of N:
  4. pN(n=4)=
  5. Find the conditional PMF of K given that N=6.
  6. pK|N(k=8|6)=
  7. Find the conditional mean and variance of K, given that he bought at least 2 but no more than 3 books.
    Conditional mean:
  8. Conditional variance:
  9. 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...