Let X and Y be continuous random variables with joint distribution function,   F (x,y).  Let g (X,Y) and h (X,Y) be functions of X and Y.   PROVE  If X and Y are independent, then E[XY] = E[X] E[Y]

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 8E
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PROOF 

Let X and Y be continuous random variables with joint distribution function,   F (x,y). 

Let g (X,Y) and h (X,Y) be functions of X and Y.  

PROVE 

If X and Y are independent, then E[XY] = E[X] E[Y] 

 

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