Transcribed text From Image: A balanced coin is tossed infinite number of times. The value of 1 is assigned to a head and the value of 2 is assigned to a tail. Suppose the random variable X representing the number of heads in tossing. a. Construct the probability distribution of X. b. Calculate the mean and variance of X. Suppose a sample of three coins is drawn from the above population. c. Construct the probability distribution of the sample mean . d. Calculate E(X) and Var(7). Show your work. e. Refer to parts (d) and (b) and verify E(X) = Hy and V(X) = V(X)/3.