Assume that \(\displaystyle X_1,X_2,...,X_n\) are iid uniform on [0,1]. Show that \(\displaystyle (X_1X_2...X_n)^\frac{1}{n}\to e^{-1}\) a.e. for \(\displaystyle n\to\infty\).(Itwasntme)

Assume that \(\displaystyle X_1,X_2,...,X_n\) are iid uniform on [0,1]. Show that \(\displaystyle (X_1X_2...X_n)^\frac{1}{n}\to e^{-1}\) a.e. for \(\displaystyle n\to\infty\).(Itwasntme)