You take a standard deck of 52 cards {four suits: spades, hearts, clubs, diamonds; thirteen ranksnct2,14,56,18,9,1U,J,G,K}. The deck is shuttled uniformly. You go through the shufed deck one card at a time and count the number of times that two consecutive cards have the same rahk. For instance, if you see A, A, 5, K, G, C], G, then you see two consecutive aces, then two consecutive queens {the first two queens), and lastly another pair of two consecutive queens {the last two queens}. [a]: For k = 1, . .. , 51, let XE be a random variable that equals 1 ifthe kth and Us -l 1)th cards in the deck have the same rank and zero otherwise. What is the expectation of Xk? {b} LetX be the total number of times that two consecutive cards have the same rank. Find the expectation of X