Define a Bernoulli process by the series of independent and identically dis- tributed random variables {X;} with i = 1..00 such that: P(X; 1) = p P(X; 0) = 1– p The event X; a) Let {Nn} be the number of successes by time n. What is P(Nn = k)? b) Let T be the time of the kth success. Show that: = 1 denotes a "success" at time i. %3D P(Tk+1 - Tk = n|To, ...,Tk) = p(1 – p)"-1 ..... c) Calculate the moment generating function: E[e*T\]

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