Hello, I am having difficulty approaching this problem:(adsbygoogle = window.adsbygoogle || []).push({});

Assume that K, Z_1, Z_2, ... are independent.

Let K be geometrically distributed with parameter success = p, failure = q.

P(K = k) = q^(k-1) * p , k >= 1

Let Z_1, Z_2, ... be iid exponentially distributed random variables with parameter (lambda).

f(z) =

(lambda)*exp(-(lambda)x) , x >= 0

0, otherwise

Find the cdf of Z_1 + Z_2 + ... + Z_K

I think there is some relation to the Gamma function here, but I'm not quite sure how...

Any hints/suggestions?

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# Summation of geometric number of iid exponentially distributed random variables

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