Finding Moments of Normal Distribution with Unknown Constant

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Homework Statement

You have i.i.d. random variables X₁,...,X_n ~ Normal ([tex]\Theta[/tex],c^2*[tex]\Theta[/tex]^2), where "c" is a known positive constant (relative variability = std. dev(X)/E[X]) and [tex]\Theta[/tex] is an unknown positive constant. Find the first four moments. E.g E[X^j] where j=1,2,3,4.

Homework Equations

The Attempt at a Solution

So i know the pdf of a normal distribution to be, and what i did was input (c*[tex]\Theta[/tex])² as the standard deviation into this. Then I took the expected value of that to get the first order moment. Is this the proper way to do it? Does having (c[tex]\Theta[/tex])² change how you integrate the expectation of a normal distribution relative to how you would for the usual N([tex]\mu[/tex],[tex]\sigma[/tex]) case?

 

[doubleshadow1]

Homework Statement

You have i.i.d. random variables X₁,...,X_n ~ Normal ([tex]\Theta[/tex],c^2*[tex]\Theta[/tex]^2), where "c" is a known positive constant (relative variability = std. dev(X)/E[X]) and [tex]\Theta[/tex] is an unknown positive constant. Find the first four moments. E.g E[X^j] where j=1,2,3,4.

Homework Equations

The Attempt at a Solution

So i know the pdf of a normal distribution to be, and what i did was input (c*[tex]\Theta[/tex])^2 as the standard deviation into this. Then I took the expected value of that to get the first order moment. Is this the proper way to do it? Does having (c[tex]\Theta[/tex])^2 change how you integrate the expectation of a normal distribution relative to how you would for the usual N([tex]\mu[/tex],[tex]\sigma[/tex]) case?

 

[doubleshadow1]

Sorry the first one i formatted poorly, and couldn't figure it out. New to this forum, just figuring stuff out.