This preview shows page 1. Sign up to view the full content.
Unformatted text preview: X and Y , one has E  XY  ≤ 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 nonnegative 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. (However, if you feel a need of continuity, you may assume that f k are continuous)....
View
Full
Document
This note was uploaded on 01/25/2011 for the course STAT 235a at Stanford.
 '07
 RomanVershynin
 Probability

Click to edit the document details