Question

Let X be the Poisson random variable with parameter $\lambda =1$, then the probability $P(0\le x\le 2)$ equals

• A. $\frac{1}{2e}$
• B. $\frac{3}{2e}$
• C. $\frac{5}{2e}$
• D. $\frac{7}{2e}$

Answer 1

The correct option is C $\frac{5}{2e}$

Poisson distribution,

$P\left(x\right)=\frac{e^{-\lambda }{\lambda }^x}{x!}$

$\because \lambda =1$

So,

$P(0\le x\le 2)=P\left(0\right)+P\left(1\right)+P\left(2\right)$

$=\frac{e^{-1}\cdot (1{)}^0}{0!}+\frac{e^{-1}\cdot (1{)}^1}{1!}+\frac{e^{-1}(1{)}^2}{2!}$

$=\frac{1}{e}+\frac{1}{e}+\frac{1}{2e}$

$=\frac{5}{2e}$