1 we have seen that a thinned poisson process is again a, Ask an Expert

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1. We have seen that a thinned Poisson process, is, again, a Poisson-process. Prove the following analog for a "geometric process." More precisely:

(a) Show that, if N and X, X1, X2, . . . are independent random variables, N ∈ Ge(α), and X ∈ Be(β), then Y = X1 + X2 + · · · + XN has a
geometric distribution, and determine the parameter.

(b) Safety check by computing mean and variance with the "usual" formu- las for mean and variance of sums of a random number of independent random variables.

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Category:- Statistics and Probability
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