In a poisson variate x, if P(x=0) = 0.2 then the variance of the distribution is 
 

Given that X follows poisson distribution and P(X=0)=0.2

$$\begin{gathered} \Rightarrow \frac{{\mathrm{e}}^{-\mathrm{\lambda }}.{\mathrm{\lambda }}^0}{0!}=0.2 \\ \Rightarrow {\mathrm{e}}^{-\mathrm{\lambda }}=0.2 \\ \Rightarrow \frac{1}{{\mathrm{e}}^{\mathrm{\lambda }}}=\frac{1}{5} \\ \Rightarrow {\mathrm{e}}^{\mathrm{\lambda }}=5 \\ \Rightarrow \mathrm{\lambda }={\log }_{e}5 \end{gathered}$$

$\therefore$ Variance $\left(\mathrm{\lambda }\right)={\log }_{e}5$