Question 4: A bag contains 80 fair coins and 20 magic coins. Flipping a fair coin results in a head with probability 0.5, whereas flipping a magic coin results in a head with probability 1.0. (a) Consider randomly drawing one coin from the bag and flipping it. What is the probability of seeing a head? (b) Consider drawing two coins from the bag with replacement and flip- ping each of them once. Let X1 = 10 if first flip a head if first flip a tail ' X2 = 1 if second flip a head 0 if second flip a tail Are X1 and X2 independent? (c) Let X denote the number of heads you see. Note that X can be 0,1,2. What is E(X)? What is V(X)? (d) Now consider drawing one coin from the bag and flipping it twice. Let if first flip a head Y1 =0 if first flip a tail , Y2 = 1 if second flip a head 0 if second flip a tail Are Y1 and Y2 independent