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Problem 5 Let AU] . . _ nl] be an array of size n. Each array entry is chosen uniformly and independently at random from one of the 52 lowercase and uppercase letters in the English alphabet, i_e_, fromthesett={a_._..z.A _____ Z}. [a] Model the random experiment (for choosing all values of array A} by giving the sample space 5'2 and the probability distribution p. [Recall that p maps each elementary event to its probability.) {b} What is the probability that the vaiue of array entry AM] is either 2 or Z? (No justi- cation required.) (c) Let random variable X denote the expected number of array entries with value a or 2'. Determine the expected value of X. and explain how you derive your answer. {d} Let E be the event that two consecutive array entries contain exactly the same symbol. |.e.r E occurs if and only if there is an index i' E {[1, . . . . n 2} such that A[i] = A[i+ 1]. For example. in the array below, event E occurs, because A[] = AP] = gr. A ; III-W Use the union bound to show that E occurs with probability less than 1/2. provided that the array A has size n = 26