2. Albert and Karle find a secret stash of 5 Key Lime, 5 Grapefruit, 5 Berry LaCroixes. Albert randomly selects 5 of these without looking . (a) (3 points ) Let X be a random variable representing the number of Grapefruit LaCroixes selected. What is the pmf of X? (Write the equation) (b) {3 points) Karle wants to find the probability that at least 3 of the LaCroixes selected will be Key Lime . (Calculate the probability ) 3. Let X ~ Binom(20,0.4). Let Y = 10X + 1. Evaluate and write your answers as a number. (a) (2 points } Find E[X] and Var[X]. (b) {3 points ) Find E[X2]. (c) (2 points ) Find E[Y] (d) {2 points ) Find Var[Y]