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Integration of a pdf, expected value 
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#1
Nov211, 09:37 AM

P: 46

1. The problem statement, all variables and given/known data
Show that E[Y^4] = 3, where Y~N(0,1) 2. Relevant equations E[(Ymu)^4]/[E(Ymu)^2]^2 = 3 E(Y^4) = 1/sprt(2pi)*intregral (y^4)*e^(y^2/2) 3. The attempt at a solution I have expanded and simplified the first equation above and cannot get it to equal 3. I think it's possible to solve the second using integration by parts but I can't find what to use for [u, du, dv, v] in order to integrate by parts. Any help would be appreciated. Thanks. 


#2
Nov211, 09:52 AM

P: 46

Sorry, it's a definite integral in from inf to inf.



#3
Nov211, 11:47 AM

Sci Advisor
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P: 5,086

RGV 


#4
Nov211, 08:46 PM

P: 46

Integration of a pdf, expected value
I tried integration by parts but the integral I end up with makes no sense to me.



#5
Nov311, 02:29 AM

Sci Advisor
HW Helper
Thanks
P: 5,086

RGV 


#6
Nov311, 07:11 AM

P: 828

Just spitballing, is there a way to use some substitutions to make this look something like the pdf of a gamma distribution? Then use what you know about that?



#7
Nov311, 08:13 PM

P: 46

I integrated the Gaussian distribution, it took a long time but I finally got the right answer. After making a substitution, integration by parts worked. I would like to know if the formula: E[(Ymu)^4]/[E(Ymu)^2]^2, is useless for answering this question though. Thanks guys.



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