Exponential random variable: prove μ=σ

**nikie1o2** · October 21st 2010, 03:39 PM

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

**mr fantastic** · October 21st 2010, 05:11 PM

Originally Posted by nikie1o2

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

What have you tried? Where are you stuck? Please show all the work you have done so far.

**pickslides** · October 21st 2010, 05:24 PM

Here's a kick start

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

Find

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

$\displaystyle SD(x) =\sqrt{Var(x)} = \sqrt{\int_0^\infty(x-E(x))^2\times f(x)~dx}$

**mr fantastic** · October 21st 2010, 05:32 PM

Originally Posted by pickslides

Here's a kick start

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

Find

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

$\displaystyle SD(x) =\sqrt{Var(x)} = \sqrt{\int_0^\infty(x-E(x))^2\times f(x)~dx}$

Personally, I would use E(X^2) - (E(X))^2 to calculate the variance. I would prefer no further help be given until the OP has shown his/her attempt and clearly stated where the difficulty is.

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