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Q)

If a random variable $X$ follows poisson distribution such that $E(X^{2})=30$ then the variance of the distribution is

\[\begin{array}{1 1}(1)6&(2)5\\(3)30&(4)25\end{array}\]

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A)
Variance $=E(X^2)-[E(X)]^2$ -------(1)
$E(X)$ is mean of X
In the case of Poisson distribution variance $=E(X) =\lambda $ (say)
(1) => $\lambda =30 -\lambda^2$
$\lambda^2+\lambda-30=0$
$(\lambda+6) (\lambda-5)=0$
$\lambda=-6\;or \; \lambda=5$
$\lambda=-6$ is not possible
$\lambda=5$
Variance =5
Hence 2 is the correct answer.
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