# Expectation of higher order moment (Bayesian Stats)

I am taking a course in Bayesian statistics, which is off my field. In the lecture notes, the instructor showed

E[X^2n] = (2n-1) σ^2n

and E[X^3 . Y] = E[Y^3 . X] = 3.ρ.σ^4

where  σ = variance

E = expectation

X is a random variable.

ρ = cor(XY) = E[XY]/σ^2

Can anyone kindly explain how these equations were derived or atleast point me towards some text where I can understand this? Is this to do with the moment generating function?

### I found the answer in Random

I found the answer in Random data analysis by Bendat.

### sHPB RESULTS

request you to please help me in SHPB model. I have some query. Firstly I will explain what I have done and then I will pose my query.
SHPB Model in ABAQUS:
A metal sample is modelled in SHPB based. After successful run of model, I have strain rate applied and the incident, transmitted and reflected strain-time history. I want to know, how can I plot the stress-strain curve of this sample? What parameters from output should I choose to plot this curve? So that I have stress-strain curve of this metal sample for the particular applied strain rate.

### Thank you for this nice article

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