Originally Posted by

**Statistik** Moo,

Sorry. Here it is:

$\displaystyle

iid: U(\theta_1, \theta_2) => MLE (\theta_1, \theta_2) = (X_{(1)}, X_{(n)})

$

$\displaystyle

f_{X_{(1)}}(x) = n * (1 - \frac {x-\theta_1} {\theta_2 - \theta_1})^{(n-1)} * \frac {1} {\theta_2 - \theta_1} $ ~ $\displaystyle

\frac {1} {\theta_2 - \theta_1} * Beta (1,n) $

I am then trying to get $\displaystyle E[X_{(1)}] $ = ? would this be $\displaystyle \frac{1} {\theta_2 - \theta_1} * \frac {1} {n+1} $ ?

For $\displaystyle X_{(n)} $, I get the same thing except the distribution is Beta (n,1) and gives $\displaystyle E[X_{(n)}] = \frac{1} {\theta_2 - \theta_1} * \frac {n} {n+1} $ ?

Thanks!