Question: Show that the jointly continuous (discrete) random variables X1, . . . ,Xn are independent if and only if their joint probability density (mass) function

Show that the jointly continuous (discrete) random variables X1, . . . ,Xn are independent if and only if their joint probability density (mass) function f (x1, . . . , xn) can be written as

for nonnegative functions gi(x), i = 1, . . . , n.

IT fxn)-ai) 1

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