Let X∼Geometric(p)X \sim \text{Geometric}(p)X∼Geometric(p) with P(X=k)=p(1−p)k−1P(X=k) = p(1-p)^{k-1}P(X=k)=p(1−p)k−1 for k=1,2,…k=1, 2, \dotsk=1,2,…. Find E[X(X−1)]E[X(X-1)]E[X(X−1)].
2(1−p)p2\frac{2(1-p)}{p^2}p22(1−p)
2(1−p)2p2\frac{2(1-p)^2}{p^2}p22(1−p)2
1−pp2\frac{1-p}{p^2}p21−p
2p2\frac{2}{p^2}p22