# Question on exponential distribution

• Jan 23rd 2013, 04:04 PM
sakuraxkisu
Question on exponential distribution
Let {X1,...,Xn} be a random sample from the exponential distribution with probability density function f(x) = (mu)^-1 exp(-x/mu) for x > 0, and 0 otherwise, where mu>0 is an unknown parameter.
a) Compute the mean and the variance of Xi.

Any help would be greatly appreciated :)
• Jan 23rd 2013, 10:12 PM
Sambit
Re: Question on exponential distribution
Just try the usual integration $\int_{0}^{\infty} xf(x) dx$ for mean and $\int_{0}^{\infty} x^2f(x) dx$ for variance.
• Jan 26th 2013, 02:51 PM
sakuraxkisu
Re: Question on exponential distribution
Hi, I did this and found that E(X)=mu, and Var(X)=mu^2. So, would E(Xi) be the sum from i=1 to k of mu i, and would Var(Xi) be the sum from i to k of (mu i)^2?
• Jan 27th 2013, 01:00 AM
Sambit
Re: Question on exponential distribution
$\mu$ and $\mu^2$ are $E(X_i)$ and $Var(X_i)$ respectively. The summation will come in the answer if you want $E(\sum_{i=1}^{n} X_i)$ and $Var(\sum_{i=1}^{n} X_i)$