Scalar property of variance and expectation

For any scalar αα, 𝔼[αX]=α𝔼[X]\mathbb{E}[αX] = α\mathbb{E}[X]. Var[αX]=α2Var[X]\mathrm{Var}[αX] = α^2 \mathrm{Var}[X].


See: Expectation, Variance

References:

  1. http://theanalysisofdata.com/probability/2_3.html
  2. https://stats.stackexchange.com/questions/184998/the-linearity-of-variance