grandes-ecoles 2017 QII.B.4

grandes-ecoles · France · centrale-maths2__official Sum of Poisson processes

Let $r$ be a non-zero natural integer and let $X_{1}, \ldots, X_{r}$ be mutually independent Poisson random variables. Show that $\sum_{i=1}^{r} i X_{i}$ is an infinitely divisible random variable.

Let $r$ be a non-zero natural integer and let $X_{1}, \ldots, X_{r}$ be mutually independent Poisson random variables. Show that $\sum_{i=1}^{r} i X_{i}$ is an infinitely divisible random variable.

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