Question

Consider a random variable to which a Poisson distribution is best fitted. It happens that $P_{x=1}=\frac{2}{3}{P}_{x=2}$ on this distribution plot. The variance of this distribution will be

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

Answer 1

The correct option is A 3

P(X = r success) $=\frac{e^{-\lambda }{\lambda }^r}{r!}$ (Poisson Distribution)

AT Q, $P(X=1)=\frac{2}{3}P(X=2)$

$\frac{e^{-\lambda }{\lambda }^1}{1}=\frac{2}{3}\frac{e^{-\lambda }{\lambda }^2}{2}$

$\Rightarrow \lambda =\frac{{\lambda }^2}{3}$

$\Rightarrow \lambda =3$

We know that in poisson distribution,

Mean = Variance

$=\lambda$

= 3