# Exponential random variable: prove μ=σ

• Oct 21st 2010, 03:39 PM
nikie1o2
Exponential random variable: prove μ=σ
Show the mean equals the standard deviation of the exponential random variable function.
• Oct 21st 2010, 05:11 PM
mr fantastic
Quote:

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.
• Oct 21st 2010, 05:24 PM
pickslides
Here's a kick start

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

Find

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

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

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.