Use the MGF of your sum and obtain a double expectation, where you condition on K.
But I need to know how you write your exponentials and also the geometric.
So, show your work.
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!