Question

If for a poisson distribution $P(X=0)=0.2$, then the variance of the distribution is

• A. $5$
• B. $lo{g}_{10}5$
• C. $lo{g}_{e}5$
• D. $lo{g}_{5}e$

Answer 1

Answer: (C)

$lo{g}_{e}5$

Poisson's distribution implies
$P(X=n)=\frac{{\lambda }^n{e}^{-\lambda }}{n!}$
Where mean=variance=$\lambda$
Hence substituting $x=0$ we get
$e^{-\lambda }=0.2$
$e^{\lambda }=5$
$\lambda =ln\left(5\right)$
Hence mean=variance=$lo{g}_e\left(5\right)$