Statistics · Statistical distributions
Chapter 1 · 3
The idea
Linear combinations of random variables
E(aX + b) and Var(aX + b), expectation and variance of aX ± bY for independent variables — variances ADD even when the variables subtract — the difference between nX and the sum of n independent copies, and combining Normal (and Poisson) variables.
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Statistics · Statistical distributions
Linear combinations of random variables
E(aX + b) and Var(aX + b), expectation and variance of aX ± bY for independent variables — variances ADD even when the variables subtract — the difference between nX and the sum of n independent copies, and combining Normal (and Poisson) variables.
Why it works
Scaling and shifting one variable
If every outcome of is transformed to :The mean is dragged along by both the stretch and the shift. The variance ignores completely — shifting every value by the same amount moves the distribution without changing its spread — and picks up , not , because variance is measured in squared units.
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