Linear Transformations of DRVs (Edexcel A-Level Further Mathematics): Flashcards

$Y = mX + c$

$E(kX) = kE(X)$

$\text{Var}(kX) = k^2 \text{Var}(X)$

$E(X + k) = E(X) + k$

$\text{Var}(X + k) = \text{Var}(X)$

$(X + Y) \sim N(\mu_x + \mu_y, \sigma_x^2 + \sigma_y^2)$

$(X - Y) \sim N(\mu_x - \mu_y, \sigma_x^2 + \sigma_y^2)$

$(X + Y) \sim Po(\lambda_x + \lambda_y)$

Mean equals variance

No, because $E(X - Y) \neq \text{Var}(X - Y)$