# “If $X$ is an exponential random variable with a mean of $m$, then $\text{Var}(X)=m^2$”-question

Been struggling to fill in the blanks... can anyone help?

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Hint: I wonder if the square root of the variance is a parameter of any importance in probability or statistics? – Dilip Sarwate Mar 7 '12 at 12:23
Is the square root of the variance the same as the standard deviation? – methuselah Mar 7 '12 at 14:21
Yes, the positive square root of the variance is called the standard deviation. What is the value of the standard deviation of an exponential random variable with mean $m$? If you still have difficulty finishing the problem you are working on (homework?), say not the struggle not availeth. – Dilip Sarwate Mar 7 '12 at 14:29
I'm thinking that it would be the root mean or am I getting the wrong gist of things? – methuselah Mar 7 '12 at 22:06
I give up. There are two blanks that you are struggling to fill in. One of them (doesn't matter whether it is the first or the second blank) should be filled in with the only four-letter word that occurs twice in the question that you posed above, while the other blank should be filled in with a two-word phrase (consisting of a eight-letter adjective qualifying a nine-letter noun) that has been used twice in the four comments above. – Dilip Sarwate Mar 7 '12 at 22:52

The exponential distribution is: $$f(x)=\lambda e^{-\lambda x}$$ If $X$ is an exponential distribuited random variable, then: $$P(X)\le x=1-e^{\lambda x}$$ and $$P(X>x)=e^{-\lambda x}$$ The expected value: $E(X)=\frac{1}{\lambda}$ and the variance is:$Var(X)=\frac{1}{\lambda^2}$
Offtopic.   – Did Mar 7 '12 at 14:26