Hello, I am having difficulty approaching this problem:

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

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

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

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 help would be greatly appreciated, thanks in advance!