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

• Jan 24th 2013, 05:03 PM
farmeruser1
Finding E(X) and V(X) of a Max function
Hey guys,
So I have $\displaystyle X_{1},...,X_{n}$ ~ Uniform ($\displaystyle 0$,$\displaystyle \theta$) where $\displaystyle \hat\theta$=max{$\displaystyle X_{1},...,X_{n}$} .
All I have to do is find Bias and se.
How Do I find the Bias and se?
Bias=E($\displaystyle \hat\theta$)-$\displaystyle \theta$
How Do I find expected value and $\displaystyle \theta$?
• Jan 24th 2013, 08:31 PM
chiro
Re: Finding E(X) and V(X) of a Max function
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).
• Jan 25th 2013, 06:07 AM
farmeruser1
Re: Finding E(X) and V(X) of a Max function
Hey chiro,
Looking at Wikipedia, It says E($\displaystyle X_{k}$)=$\displaystyle k/(n+1)$
So How would I find the Biad?
Bias=E($\displaystyle n/(n+1)$+$\displaystyle \theta$?
• Jan 25th 2013, 03:48 PM
chiro
Re: Finding E(X) and V(X) of a Max function
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.