Show the mean equals the standard deviation of the exponential random variable function.

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- Oct 21st 2010, 03:39 PMnikie1o2Exponential random variable: prove μ=σ
Show the mean equals the standard deviation of the exponential random variable function.

- Oct 21st 2010, 05:11 PMmr fantastic
- Oct 21st 2010, 05:24 PMpickslides
Here's a kick start

For $\displaystyle \displaystyle f(x) = \lambda e^{-\lambda x}$

Find

$\displaystyle \displaystyle E(x) = \int_0^\infty x\times f(x)~dx$

$\displaystyle \displaystyle SD(x) =\sqrt{Var(x)} = \sqrt{\int_0^\infty(x-E(x))^2\times f(x)~dx}$ - Oct 21st 2010, 05:32 PMmr fantastic