You take a standard deck of 52 cards [four suits: spades, hearts, ctubs, diamonds; thirteen ranksht, 1, 2,3, 4, 5, 6,1 S,Q,1D,J, G, K}. The deck is shuttled uniformly. You go through the shuffled deck one card at a time and count the number of times that two consecutive cards have the same rank. For instance, if you see A, A, 5, K, 0, {1,11}, then you see two consecutive aces, then two consecutive queens {the first two queens}, and iastty another pair of two consecutive queens {the test two queens}. [a]: For k = 1,. .. ., 51,1et X;- be a random variable that equals 1 ifthe kth and [R'- -i 1}th cards in the deck have the same rank and zero otherwise. What is the expectation of IQ? {bi Let X be the total number of times that two consecutive cards have the same rank. Find the expectation of X