scalar property of variance and expectation

Proposition

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

See also

• expectation
  • follows from linearity of expectation
• variance

References:

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