Let X∼Geometric(p)X \sim \text{Geometric}(p)X∼Geometric(p) with P(X=k)=(1−p)k−1pP(X=k) = (1-p)^{k-1}pP(X=k)=(1−p)k−1p for k=1,2,…k=1, 2, \dotsk=1,2,…. What is the variance Var(X)Var(X)Var(X)?
1−pp2\frac{1-p}{p^2}p21−p
p(1−p)2\frac{p}{(1-p)^2}(1−p)2p
1−pp\frac{1-p}{p}p1−p
p21−p\frac{p^2}{1-p}1−pp2