grandes-ecoles 2023 Q9

grandes-ecoles · France · mines-ponts-maths2__psi Probability Generating Functions Explicit computation of a PGF or characteristic function
We denote by $G_{X_n}$ and $G_Y$ the generating functions of the variables $X_n$ and $Y$ from the previous question, respectively. Express $G_{X_n}(s)$ as a sum, for $s$ real, and verify that $$\forall s \in \mathbf{R} \quad \lim_{n \rightarrow +\infty} G_{X_n}(s) = G_Y(s)$$ 
We denote by $G_{X_n}$ and $G_Y$ the generating functions of the variables $X_n$ and $Y$ from the previous question, respectively. Express $G_{X_n}(s)$ as a sum, for $s$ real, and verify that
$$\forall s \in \mathbf{R} \quad \lim_{n \rightarrow +\infty} G_{X_n}(s) = G_Y(s)$$
Paper Questions
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