Скачать или смотреть Prob & Stats, Lec 8A: Standardizing a Random Variable (Z=(X - μ)/σ has mean 0 and variance 1)

If X is a random variable with mean μ and standard deviation σ, the transformed random variable Z = (X - μ)/σ (standardized RV) has mean 0 and variance 1 (and standard deviation 1). Properties of expected value help us prove this. 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 8, Part 1. Also for Data Scientists and Actuarial Science majors.

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