Show that the random variables X1, . . . , Xn are independent if for each i =

2, . . . , n, Xi is independent of X1, . . . , Xi−1.

Hint: X1, . . . , Xn are independent if for any sets A1, . . . , An

On the other hand Xi is independent of X1, . . . , Xi−1 if for any sets A1, . . . , Ai

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n P(X Aj, j = 1, ..., n) = [] P(X A) j=1