In: Statistics and Probability
Let X be the number of heads in two tosses of a fair coin. Suppose a fair die is rolled X+1 times after the value of X is determined from the coin tosses. Let Y denote the total of the face values of the X+1 rolls of the die. Find E[Y | X = x] and V[Y | X = x] as expressions involving x. Use these conditional expected values to find E[Y] and V[Y].