Linear Transformation of Random Variables
Y = aX + b
i.i.d. = “independent and identically distributed”
Y will have the same distribution shape as X.
If X has a normal distribution then Y will also be normally distributed.
If X has a discrete probability distribution, the corresponding values of Y will also have the same probabilities
New… | y = X + b | y = a * X | y = a * X + b |
|---|---|---|---|
…Mean | μ(y) = μ(X) + b | μ(y) = a * μ(X) | μ(y) = a * μ(X) + b |
…Standard Deviation | σ(y) = σ(X) | σ(y) = a * σ(X) | σ(y) = a * σ(X) |
…Variance | σ²(y) = σ²(X) | σ²(y) = a² * σ²(X) | σ²(y) = a² * σ²(X) |