L18_Prod_Exp

L18_Prod_Exp - Illustration of the Proof of Lemma 5.28...

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Unformatted text preview: Illustration of the Proof of Lemma 5.28 Version 2.1: Last updated, Nov 24, 2007 In class, we proved that the expectation of the product of two independent random variables, is the product of their expectations . Formally In class, we proved that the expectation of the product of two independent random variables, is the product of their expectations . Formally Lemma 5.28 If X and Y are independent random variables on sample space S with values x 1 ,x 2 ,...,x k and y 1 ,y 2 ,...,y m , respectively, then E ( XY ) = E ( X ) E ( Y ) . In class, we proved that the expectation of the product of two independent random variables, is the product of their expectations . Formally In these sides, we illustrate the proof of Lemma 5.28 with an example . Lemma 5.28 If X and Y are independent random variables on sample space S with values x 1 ,x 2 ,...,x k and y 1 ,y 2 ,...,y m , respectively, then E ( XY ) = E ( X ) E ( Y ) . Suppose that we have two independent random variables, X,Y that each can take on the values 1 , 2 , 4 , but with different probability weights. Suppose that we have two independent random variables, X,Y that each can take on the values...
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L18_Prod_Exp - Illustration of the Proof of Lemma 5.28...

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