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 $\displaystyle \theta$?

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).

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($\displaystyle n/(n+1)$+$\displaystyle \theta$?

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.