Alice is going shopping for statistics books for H hours, where I is a random variable, equally likely to be 1, 2 or 3. The number of books B she buys is random and depends on how long she is in the store for. We are told that Pr(B = b | H = h) = for b = 1, .. ., h, for some constant c. (a) [3 Points] Compute c. You may want to use one of the axioms of probability. (b) [3 Points] Find the joint distribution of B and H using the chain rule. (c) [5 Points] Find the marginal distribution of B. (d) [3 Points] Find the conditional distribution of H given that B = 1 (i.e., Pr(H = h|B = 1) for each possible h in 1,2,3). Use the definition of conditional probability and the results from previous parts