Finding E(X) and V(X) of a Max function

**farmeruser1** · January 24th 2013, 05:03 PM

Hey guys,
So I have $X_{1},...,X_{n}$ ~ Uniform ( $0$ , $\theta$ ) where $\hat\theta$ =max{ $X_{1},...,X_{n}$ } .
All I have to do is find Bias and se.
How Do I find the Bias and se?
Bias=E( $\hat\theta$ )- $\theta$
How Do I find expected value and $\theta$ ?

**chiro** · January 24th 2013, 08:31 PM

Hey farmeruser1.

Do you have the distribution of the order statistic of the uniform distributions (the maximum)? (This will help solve all the problems in this question).

**farmeruser1** · January 25th 2013, 06:07 AM

Hey chiro,
Looking at Wikipedia, It says E( $X_{k}$ )= $k/(n+1)$
So How would I find the Biad?
Bias=E( $n/(n+1)$ + $\theta$ ?

**chiro** · January 25th 2013, 03:48 PM

What is the distribution of the order statistic (maximum)? You need this in order to proceed (especially for the variance of the estimator).

Your bias is calculated as E[theta_hat] - theta.

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