grandes-ecoles 2017 QIII.A.6

grandes-ecoles · France · centrale-maths2__mp Probability Generating Functions PGF of sum of independent variables

Let $X$ and $Y$ be two independent random variables, defined on the space $\Omega$ and taking values in $\mathbb{N}$, and let $H_{X}$ and $H_{Y}$ be their auxiliary power series. Show $H_{X+Y}(t) = H_{X}(t) + H_{Y}(t)$ for all real $t$ satisfying $|t| < \min(\rho(X), \rho(Y))$.

Let $X$ and $Y$ be two independent random variables, defined on the space $\Omega$ and taking values in $\mathbb{N}$, and let $H_{X}$ and $H_{Y}$ be their auxiliary power series. Show $H_{X+Y}(t) = H_{X}(t) + H_{Y}(t)$ for all real $t$ satisfying $|t| < \min(\rho(X), \rho(Y))$.

Paper Questions

QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.B.1 QI.B.2 QII.A.1 QII.A.2 QII.A.3 QII.B.1 QII.B.2 QII.B.3 QII.B.4 QII.C.1 QII.C.2 QII.C.3 QIII.A.1 QIII.A.2 QIII.A.3 QIII.A.4 QIII.A.5 QIII.A.6 QIII.B.1 QIII.B.2 QIII.B.3 QIII.C.1 QIII.C.2 QIII.C.3 QIII.C.4 QIII.C.5