# Exponential Distribution Question

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• Oct 28th 2009, 09:22 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
• Oct 28th 2009, 10:02 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.
• Oct 28th 2009, 11:19 AM
matheagle
IF $X_1,X_2,...$ are iid then

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

or $\lambda$ or $\beta$
• Oct 28th 2009, 11:31 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)
• Oct 28th 2009, 12:03 PM
matheagle
They are the same, $\lambda=1/\beta$ use whatever your book is using.
• Oct 28th 2009, 12:04 PM
statmajor
That clears that up. Thanks.