grandes-ecoles 2017 QI.A.3

grandes-ecoles · France · centrale-maths2__mp Probability Generating Functions Infinite divisibility and decomposability via PGF

Let $X$ be a random variable following the binomial distribution $\mathcal{B}(n, p)$ where $n \geqslant 1$ and $p \in ]0,1[$. Show that $X$ is decomposable if and only if $n \geqslant 2$.

Let $X$ be a random variable following the binomial distribution $\mathcal{B}(n, p)$ where $n \geqslant 1$ and $p \in ]0,1[$. Show that $X$ is decomposable if and only if $n \geqslant 2$.

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