Let X follow geometric distribution with probability of succ

Let X follow geometric distribution with probability of success p, where P(X=x)=q^(x-1)p, where q=1-p

a) Verify it is a pdf

b) Calculate the probability P(X>s), where s is an integer

c) Using part(b) prove the memory less property, i.e. P(X>s+t | X>t)=P(X>s) where s and t are integers.

Solution