Please give me a solution for each question. Thank you.

Suppose I have four fair coins, two which have a head on both sides, one which has a tail on both sides, and one which is normal {a head on one side and a tail on the other side). (a) I shut my eyes, pick one of the four coins at random, and ip it. What is the probability that the lower face of the coin is a head? (b) I open my eyes and see that the coin is showing heads (on the upper face). What is the probability that the lower face is a head? Suppose the random variable X has the following probability distribution: :1: 0 1 2 p(:r) 0.6 0.3 0.1 Calculate the following (do it manually rst, then try doing it in R using the sum func tion): (a) E(X (b) V(X (c)E( W( ) ) X) f \"7)