Question

In a Poisson distribution if $P(X=2)=P(X=3)$ then the value of its parameter $\lambda$ is

• A. $6$
• B. $2$
• C. $3$
• D. $0$

Answer 1

The correct option is C $3$

According to Poisson distribution,
$P(x=k)=\frac{{\lambda }^k{e}^{-\lambda }}{k!}$.
Hence
$P(x=2)=P(x=3)$ implies
$\frac{{\lambda }^2{e}^{-\lambda }}{2!}=\frac{{\lambda }^3{e}^{-\lambda }}{3!}$
$\frac{1}{2}=\frac{{\lambda }^{3-2}}{6}$
$\lambda =\frac{6}{2}=3$.