PGFs of Sums & Transformations (Edexcel A-Level Further Mathematics): Flashcards

$G_Z(t) = G_X(t) \times G_Y(t)$

$G_Z(t) = G_X(t^a)$

$G_Z(t) = t^c G_X(t)$

$\mathbb{E}[Z] = \mathbb{E}[X] + \mathbb{E}[Y]$

$\text{Var}(Z) = \text{Var}(X) + \text{Var}(Y)$

$G_X(t) = e^{\lambda(t-1)}$

$G_X(t) = [pt + (1-p)]^n$

$G_X(t) = \frac{p}{1-(1-p)t}$

When $X$ and $Y$ are independent

$\text{Po}(\lambda_1 + \lambda_2)$