For a poisson variate $X$, if $P(X=2)=3 P(X=3)$, then the mean of $X$ is :

Question

Aicharya · Accepted Answer

We know that, $P(X=k)=\frac{\lambda^k e^\lambda}{k !}$ Since, $P(X=2)=3 P(X=3)$ $\Rightarrow \quad \frac{\lambda^2 e^\lambda}{2 !}=3 \cdot \frac{\lambda^3 e^\lambda}{3 !} \Rightarrow \lambda=1$ $	herefore$ Mean of poisson distribution $=\lambda$ $=1$

For a poisson variate $X$, if $P(X=2)=3 P(X=3)$, then the mean of $X$ is :

Solution