Question

The number of car accidents in a day follow Poisson distribution with $E\left(X^2\right)=12.$ then the expected number of car accidents in a day are _______.

• A. 3

Answer 1

The correct option is A 3
$\begin{array}{cc}\text{For Poisson distribution:}& \\ \text{Mean}& =\text{Variance}=\lambda \\ \because Var\left(X\right)& =E\left(X^2\right)-\left[E\right(X){]}^2\\ \lambda & =12-{\lambda }^2\\ {\lambda }^2+\lambda -12& =0\\ (\lambda +4)(\lambda -3)& =0\\ \lambda & =3,\lambda \ne -4\\ \text{So,}‘\lambda & =3\end{array}$