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January 27th, 2017, 10:58 PM   #1
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Affine transformation

Hi guys am stuck on this one

If $E(X)=3$ and $Var(X)=2$
what is $E((2+5X)^2)$
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January 27th, 2017, 11:05 PM   #2
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$E[(2+5X)^2] = E[4+10X + 25X^2] = 4 + 10E[X] + 25 E[X^2]$

$E[X^2] = Var[X] + (E[X])^2 = 2 + 3^2 = 11$

$4 + 10E[X] + 25 E[X^2] = 4 + 10(3) + 25(11) = 309$
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January 27th, 2017, 11:23 PM   #3
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Quote:
Originally Posted by romsek View Post
$E[(2+5X)^2] = E[4+10X + 25X^2] = 4 + 10E[X] + 25 E[X^2]$

$E[X^2] = Var[X] + (E[X])^2 = 2 + 3^2 = 11$

$4 + 10E[X] + 25 E[X^2] = 4 + 10(3) + 25(11) = 309$
I ll replace the 10 with 20 on the distribution. You are a superstar man. Thanks a bunch
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