Question

A random variable X has Poisson distribution with mean 2. Then $P(X >\, 1.5)$ equals :

• A. $\frac{3}{e^{2}}$
• B. $1-\frac{3}{e^{2}}$
• C. $0$
• D. $\frac{2}{e^{2}}$

Answer 1

Answer: (B)

Key Idea : In a poisson distribution,
$P\left(X = r\right) = \frac{e^{-\lambda}\lambda^{r}}{r}\quad\left(\lambda = mean\right).$
$\therefore \quad P\left(X = r > 1.5\right) = P\left(2\right)+P\left(3\right) + ...\infty$
$= 1-\left(\left(P\left(0\right)+P\left(1\right)\right)\right)$
$= 1-\left(e^{-2}+\frac{e^{-2}\times2}{1}\right) = 1-\frac{3}{e^{2}}$