Please show the work thank you !

Problem 2.3 (10 points) Assume the number B of blossoms on an apple tree is Poisson dis- tributed with parameter A > 0 and suppose that, independently from all the others, each blossom will yield a fruit with probability p = 1/2. (a) Compute the probability mass function p A of the number of apples A on the tree. Hint: Recall the fact (from a math class or stats class) that 00 Ak 2 F = 6A (A e R). k=0 ' (b) Compute the conditional probability mass function of B given the number of apples A. (c) Find the variance of the number of apples A