Suppose, you have have n letters addressed to n separate individuals, and have n envelopes with the names and addresses of the recipients written on them. Suppose, you put the letters randomly in the envelopes. Let Xi, i = 1,..., n be the random variables such that X; = 1 if i th letter goes to the correct envelope and X; = 0 otherwise.a) Show that X; follows Bernoulli(1/n).b) Suppose, X be the total number of letters that are placed in the correct envelopes. Write X in terms of X;'s and then calculate E[X].c) Are Xi, X; are independent for i + j.