Exponential Distribution Question

Printable View

October 28th 2009, 08:22 AM
statmajor

Exponential Distribution Question

Let X be teh mean of a random sample from the exponential distribution $Exp(\theta)$

Show that X is an unbiased point estimater of $\theta$

Which PDF of the exponential function do I use?

http://upload.wikimedia.org/math/6/e...a2d2ada3ca.png or http://upload.wikimedia.org/math/d/c...ece9bf0783.png
October 28th 2009, 09:02 AM
theodds

The sample mean is an unbiased estimator for the true mean. For which of those distributional forms is the defining parameter the mean? That should give you the answer.
October 28th 2009, 10:19 AM
matheagle

IF $X_1,X_2,...$ are iid then

$E(\bar X)=\mu$ which is $\theta$ in this case

or $\lambda$ or $\beta$
October 28th 2009, 10:31 AM
statmajor

Quote:

Originally Posted by matheagle

IF $X_1,X_2,...$ are iid then

$E(\bar X)=\mu$ which is $\theta$ in this case

or $\lambda$ or $\beta$

That part I got I wasnt sure which one of the PDF I needed to use, since the one with lambda's expectation is 1/lambda (according to wikipedia)
October 28th 2009, 11:03 AM
matheagle

They are the same, $\lambda=1/\beta$ use whatever your book is using.
October 28th 2009, 11:04 AM
statmajor

That clears that up. Thanks.

All times are GMT -8. The time now is 09:35 AM.