education

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 was solving the following question and I derived the Auto correlation function and proved that it is a WSS process. However, I am not sure how to go about finding the Marginal probability density function. Should I find joint probability of a and b and then find marginal probability of each random variable?

Does anyone have experience in using RAMs software applications?

I am working on a paper that looks at the limitations of managing risk and improving reliability of engineering assets by using RAMs software applications but I have no experience in using any RAMs software application.

Software applications are good for storing data and interpreting that data based on a predefined set of rules. However, recommendations made by such an application will only be as be based solely on the data available to the application.

Are there analytical expressions for computing von Mises or equivalent stress at any point for Beam elements similar to the ones in continuum elements? I would like to design a structure with beam elements and ensure that the equivalent stress is within bounds (yield stress etc) for the structure to be safe.