My Math Forum Affine transformation

 January 27th, 2017, 10:58 PM #1 Member   Joined: Jan 2017 From: California Posts: 79 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 27th, 2017, 11:05 PM #2 Senior Member     Joined: Sep 2015 From: CA Posts: 1,300 Thanks: 664 $E[(2+5X)^2] = E[4+10X + 25X^2] = 4 + 10E[X] + 25 E[X^2]$ $E[X^2] = Var[X] + (E[X])^2 = 2 + 3^2 = 11$ $4 + 10E[X] + 25 E[X^2] = 4 + 10(3) + 25(11) = 309$ Thanks from dthiaw
January 27th, 2017, 11:23 PM   #3
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Joined: Jan 2017
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Quote:
 Originally Posted by romsek $E[(2+5X)^2] = E[4+10X + 25X^2] = 4 + 10E[X] + 25 E[X^2]$ $E[X^2] = Var[X] + (E[X])^2 = 2 + 3^2 = 11$ $4 + 10E[X] + 25 E[X^2] = 4 + 10(3) + 25(11) = 309$
I ll replace the 10 with 20 on the distribution. You are a superstar man. Thanks a bunch

 Tags affine, transformation