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Unformatted text preview: X and Y , one has E | X-Y | ≤ 1 2 . 5. Independence Let X 1 ,...,X n be random variables such that P ( ( X 1 ,...,X n ) ∈ A ) = Z A f ( x ) dx for every Borel set A in R n . Assume that f : R n → R can be factored as f ( x 1 ,...,x n ) = f 1 ( x 1 ) ··· f n ( x n ) for some non-negative measurable functions f k ; R → R . Prove that X 1 ,...,X n are independent. Note that f k are not assumed to be density functions. (How-ever, if you feel a need of continuity, you may assume that f k are continuous)....
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This note was uploaded on 01/25/2011 for the course STAT 235a at Stanford.