plz answer the whole question

Problem 5 Let A[U. . . nl] be an array of size :1. 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.. from the set L = {a ..... z.A ..... Z}. (a) Model the random experiment (fer choosing all values of array A) by giving the sample space Q and the probability distribution ,0. (Recall that p maps each elementary event to its probability.) (b) What is the probability that the value of array entry A[0] is either 2 or Z? (No justifi- cation required.) (c) Let random variable X denote the expected number of array entries with value 2 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., E occurs if and only if there is an index i E {0 ..... n 2} such that A[i] = A[i + 1]. For example, in the array below, event E occurs. because ADE] = A[7] = g. A: IlIlEl-I Use the union bound to show that E occurs with probability less than 1X2. provided that the array A has size n = 26