grandes-ecoles 2020 Q9

grandes-ecoles · France · centrale-maths1__psi Poisson distribution

Deduce that, when $n$ tends to $+\infty$, $$P\left(S_n > n\right) \sim \frac{\mathrm{e}^{-n/2}}{n!} \left(\frac{n}{2}\right)^n.$$

Deduce that, when $n$ tends to $+\infty$,
$$P\left(S_n > n\right) \sim \frac{\mathrm{e}^{-n/2}}{n!} \left(\frac{n}{2}\right)^n.$$