Question

If a random variable $X$ has a poisson distributionsuch that $P(X=1)=P(X=2)$, its mean and varianceare

• A. $1,1$
• B. $2,2$
• C. $2,3$
• D. $2,4$

Answer 1

The correct option is B $2,2$

In Poisson distribution such that $P(X=1)=P(X=2)$
$P(x;\mu )=\frac{e^{-\mu }{\mu }^x}{x!}$
=> $P(1;\mu )=P(2;\mu )$
=> $\frac{e^{-\mu }{\mu }^1}{1!}=\frac{e^{-\mu }{\mu }^2}{2!}$
=> $1=$ $\frac{\mu }{2}$
=> $\mu =2$
In Poisson distribution Variance $\left(m\right)$ is equal to mean.
Mean = Variance = $2$