Question 2. [3 + 3 + 3 pts] Let (Xn)n21 be a sequence of independent Bernoulli random variables with success probability p. Denote by S? the number of failures until the first success, by S? the number of failures between the first and second sucess, and, in general, by Sk the number of failures between the (k-1)th and the kth success. (a) Comput

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Question 2. [3 + 3 + 3 pts] Let (Xn)n21 be a sequence of independent Bernoulli random variables with success probability p. Denote by S? the number of failures until the first success, by S? the number of failures between the first and second sucess, and, in general, by Sk the number of failures between the (k-1)th and the kth success. (a) Compute the joint probability mass function of S?, ..., Sn. (b) Are the random variables S?,..., Sn independent? Prove or disprove. (c) Compute the cdf of U = max{S?,. max{S?,..., Sn}.

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