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January 27th, 2017, 11:58 PM  #1 
Member Joined: Jan 2017 From: California Posts: 80 Thanks: 8  Affine transformation
Hi guys am stuck on this one If $E(X)=3$ and $Var(X)=2$ what is $E((2+5X)^2)$ 
January 28th, 2017, 12:05 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,657 Thanks: 842 
$E[(2+5X)^2] = E[4+10X + 25X^2] = 4 + 10E[X] + 25 E[X^2]$ $E[X^2] = Var[X] + (E[X])^2 = 2 + 3^2 = 11$ $4 + 10E[X] + 25 E[X^2] = 4 + 10(3) + 25(11) = 309$ 
January 28th, 2017, 12:23 AM  #3 
Member Joined: Jan 2017 From: California Posts: 80 Thanks: 8  

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