# Moments part 2 - basics

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• September 16th 2012, 09:46 PM
TheCountador
Moments part 2 - basics
Given
Mx(t) = exp(t^2 + 2t)
My(t) = exp(3t^2 + t)

Find the mgf of X + 2Y.
___________________________
Can anybody explain how
My(2t) = exp(12t^2 + 2t) ???? I figured this going backwards from the answer...so it may be wrong...

THANKS
____________
The answer is exp(13t^2 + 4t)
• September 17th 2012, 07:39 AM
harish21
Re: Moments part 2 - basics
Quote:

Originally Posted by TheCountador
Given
Mx(t) = exp(t^2 + 2t)
My(t) = exp(3t^2 + t)

Find the mgf of X + 2Y.
___________________________
Can anybody explain how
My(2t) = exp(12t^2 + 2t) ???? I figured this going backwards from the answer...so it may be wrong...

THANKS
____________
The answer is exp(13t^2 =4t) that should be a + instead of an = sign

$E[e^{t(X+2Y)}]=E[e^{tX+2tY}]=E[e^{tX}]E[e^{(2t)Y}]=e^{[t^2+2t]}\times e^{[3(2t)^2+(2t)]}=...$