Question

If $X$ is a Poisson variate with parameter $\frac{3}{2}$, find $P(X\ge 2)$

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

Answer 1

The correct option is B $1-\frac{5}{2}{e}^{\frac{-3}{2}}$

Here $\lambda =\frac{3}{2}$
$\therefore P(X\ge 2)=1-P(X=0)-P(X=1)$
$=1-\frac{e^{-3/2}(3/2{)}^0}{0!}-\frac{e^{-3/2}(3/2{)}^1}{1!}=1-\frac{5}{2}{e}^{-3/2}$