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Postdoc Position in Stochastic Simulation and Uncertainty Quantification for Solid/Structural Mechanics at Johns Hopkins University

The Shields Uncertainty Research Group (SURG) in the Dept. of Civil Engineering at Johns Hopkins University is seeking applications for the position of Postdoctoral Fellow. The postdoc will work on an Office of Naval Research (ONR) funded project developing novel stochastic simulation methodologies for quantification and propagation of uncertainty in computational solid/structural mechanics. Candidates must possess a Ph.D. in Civil Engineering, Mechanical Engineering, Applied Mathematics or a related field.

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?

What is "randomness"?

Does the word "randomness" have antonym? If yes, what is it? Why? What view of randomness does that imply?

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