If $X$ has an exponential distribution with mean $3$, then the variance of $X$…

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If $X$ has an exponential distribution with mean $3$, then the variance of $X$ is

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For exponential distribution:

Mean $= \frac{1}{\lambda}$

Variance $= \frac{1}{\lambda^2}$

Given mean $=3 \Rightarrow \lambda=\frac{1}{3}$

Variance $=\frac{1}{(1/3)^2}=9$

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