answer all questions with explanation

Problem 2.2. (10 points) Assume the number 3 of blossoms on an apple tree follows a PoissonUt) distribution for some A > 0.1 Additionally, suppose that each blossom will yield an apple with probability 1f2, and that whether each blossom yields an apple is independent of the number of blossoms and whether each other blossom yields an apple. (a) (3 points) Denote the number of apples on the tree by A. Find the probability mass function of A. (b) (3 points) Compute the probability mam function of B given the number of apples A. (c) (4 points) Calculate Var(A)