Question

If in a poisson distribution $P(X=1)=P(X=2)$; the mean of the distribution $f\left(x\right)=e^{-x}\frac{{\lambda }^x}{\angle x}$ is

• A. $1$
• B. $2$
• C. $\frac{1}{2}$
• D. $\frac{3}{2}$

Answer 1

The correct option is B $2$

Poisson's distribution implies
$P(X=n)=\frac{{\lambda }^n{e}^{-\lambda }}{n!}$
Where mean=variance=$\lambda$
Hence $P(x=1)=P(x=2)$
$\frac{{\lambda }^1{e}^{-\lambda }}{1!}=\frac{{\lambda }^2{e}^{-\lambda }}{2!}$
$\lambda =2$
Hence mean=variance=$2$