crg123's blog

How to use non-dimensional form in open source codes instead of Units

I am using an open source FEM platform, which requires you to convert your equation system to non-dimensional form. So, there are no units specified for the parameters in the problem. If you use compatible input units, you should expect the output in matching unit - just like one would do in a normal python or C++ code for solving physical problems. I have an elasto-plastic dynamic problem to solve, and these are the parameters for the Drucker-Prager Soil Model for soft clay.

E = 5000000;                 // Young's Modulus in N/m^2 or Pa

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?

Marginal Probability Density Function of Stochastic Process

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? 