Let XXX and YYY be independent geometric random variables with P(X=k)=p(1−p)k−1P(X=k) = p(1-p)^{k-1}P(X=k)=p(1−p)k−1. What is P(X=Y)P(X=Y)P(X=Y)?
p / (2-p)
p^2 / (1-(1-p)^2)
p / (2+p)
1 / (2-p)