Sum of a geometric number of independent geometric random variables. Let Y = X1 + ... + XN . where the random variables X, are geometric with parameter p. and N is geometric with parameter q. Assume that the random variables N, X1 . X2 . . .. are independent. Show. without using transforms, that Y is geometric with parameter pq. Hint: Interpret the various random variables in terms of a split Bernoulli process.
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