Question

Let x have a poisson distribution with a variance of 3. find p(x = 2).

Answer 1

Since the variance of a Poisson distribution with rate parameter $\lambda$ is $\lambda^2$, we know that $\lambda=\sqrt3$. So,

$\mathbb P(X=2)=\dfrac{e^{-\sqrt3}(\sqrt3)^2}{2!}=\dfrac3{2e^{\sqrt3}}\approx0.2654$