- #1
redflame34
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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.
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?
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?