How can we prove that using this given information:

Let f be a density function of F of X = (X1, ..., Xn). If X1, ..., Xn are indepen dent, then f (1, ..., Xn) = fx1 (21) . . . fxn(In). Theorem 1. If X1 and X2 are independent, then we have E[X1X2] = [EXI][EX2]