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

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

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

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

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

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

$\text{Po}(8)$

$4.8$

$\frac{0.5}{1-0.5t^2}$

$\prod_{i=1}^n G_{X_i}(t)$

When $X$ and $Y$ are independent