# Exponential Distribution Question

• Oct 28th 2009, 08:22 AM
statmajor
Exponential Distribution Question
Let X be teh mean of a random sample from the exponential distribution $\displaystyle Exp(\theta)$

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

Which PDF of the exponential function do I use?

• Oct 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.
• Oct 28th 2009, 10:19 AM
matheagle
IF $\displaystyle X_1,X_2,...$ are iid then

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

or $\displaystyle \lambda$ or $\displaystyle \beta$
• Oct 28th 2009, 10:31 AM
statmajor
Quote:

Originally Posted by matheagle
IF $\displaystyle X_1,X_2,...$ are iid then

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

or $\displaystyle \lambda$ or $\displaystyle \beta$

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