# Thread: Exponential random variable: prove μ=σ

1. ## Exponential random variable: prove μ=σ

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

2. 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.

3. Here's a kick start

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

Find

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

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

4. Originally Posted by pickslides
Here's a kick start

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

Find

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

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