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Unformatted text preview: for P ( { ω : X ( ω ) is in A and Y ( ω ) is in B } ) and similarly for the right hand side. In the discrete case, if we have independence, p X,Y ( x,y ) = P ( X = x,Y = y ) = P ( X = x ) P ( Y = y ) = p X ( x ) p Y ( y ) . In other words, the joint density p X,Y factors. In the continuous case, Z b a Z d c f X,Y ( x,y ) dy dx = P ( a ≤ X ≤ b,c ≤ Y ≤ d ) = P ( a ≤ X ≤ b ) P ( c ≤ Y ≤ d ) = Z b a f X ( x ) dx Z d c f Y ( y ) dy. 35...
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This note was uploaded on 12/29/2011 for the course MATH 316 taught by Professor Ansan during the Spring '10 term at SUNY Stony Brook.
 Spring '10
 ansan

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