grandes-ecoles 2017 QII.B.2

grandes-ecoles · France · centrale-maths2__mp Sum of Poisson processes

Let $n$ be a non-zero natural integer and let $X_{1}, \ldots, X_{n}$ be mutually independent random variables following Poisson distributions with respective parameters $\lambda_{1}, \ldots, \lambda_{n}$. Show that $X_{1} + \cdots + X_{n}$ follows a Poisson distribution with parameter $\lambda_{1} + \cdots + \lambda_{n}$.

Let $n$ be a non-zero natural integer and let $X_{1}, \ldots, X_{n}$ be mutually independent random variables following Poisson distributions with respective parameters $\lambda_{1}, \ldots, \lambda_{n}$. Show that $X_{1} + \cdots + X_{n}$ follows a Poisson distribution with parameter $\lambda_{1} + \cdots + \lambda_{n}$.

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