Prove that for all random variable \(X\), and any real numbers \(a\), \(b\),
\[\mathrm{E}(aX + b) = a\mathrm{E}(X) + b\]
and
\[\mathrm{Var}(aX + b) = a^2\mathrm{Var}(X)\]

Prove that for all random variable \(X\), and any real numbers \(a\), \(b\),

\[\mathrm{E}(aX + b) = a\mathrm{E}(X) + b\]

\[\mathrm{Var}(aX + b) = a^2\mathrm{Var}(X)\]

Linear Combination of Random Variables

Discrete Random Variables (DRV)

International Baccalaureate Higher Level Mathematics

Properties of expectation and variance

Properties of expectation and variance