Prob & Stats, Lec 7A: Properties of Expectation & Variance (Derive Variance Computational Formula)

Описание: The abstract rules for expected values include: 1) E[c]=c, 2) E[cX]=cE[X], 3) E[X+Y]=E[X]+E[Y]. Since Var(X)=E[(X-μ)^2] and (X-μ)^2=X^2-2μX+μ^2, we can use these to derive the variance computational formula Var(X)=E[X^2]-(E[X])^2. Variance also satisfies the laws: 1) Var(c)=0, 2) Var(cX)=c^2*Var(X), 3) Var(X+Y)=Var(X)+Var(Y) when X and Y are independent random variables. Care must be taken for the corresponding rules for standard deviations, since the square root of a sum is NOT the sum of the square roots. https://amzn.to/3rjDOoA (Probability and Statistics with Applications: A Problem Solving Text, by Asimow and Maxwell)

Calculus-based Probability and Statistics for Engineers and Scientists, Lecture 7, Part 1. Also for Data Scientists and Actuarial Science majors.

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