Let X1,X2,…,XnX_1, X_2, \dots, X_nX1,X2,…,Xn be i.i.d. Uniform(0,1)\text{Uniform}(0, 1)Uniform(0,1) random variables. Find the variance of their product P=∏i=1nXiP = \prod_{i=1}^n X_iP=∏i=1nXi.
3−n−4−n3^{-n} - 4^{-n}3−n−4−n
2−n−3−n2^{-n} - 3^{-n}2−n−3−n
12−n12^{-n}12−n
3−n−2−2n3^{-n} - 2^{-2n}3−n−2−2n