Question: If X is an Exp(1) random variable, set Z = [X] (recall the ceiling function . means round up to the next integer, so that

If X is an Exp(1) random variable, set Z = [X] (recall the ceiling function . means round up to the next integer, so that [4.231] = 5, [2] = 2 and [-1.3] = -1). a) What is the range of values taken by Z? b) Find the p.m.f. of Z; c) Show that Z has a geometric distribution and identify the parameter

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