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#1

$Old$ October 28th, 2009, 09:22 AM

statmajor $statmajor is offline$

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$Default$ 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?

or

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#2

$Old$ October 28th, 2009, 10:02 AM

theodds $theodds is offline$

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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.

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$Old$ October 28th, 2009, 11:19 AM

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

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

or $\lambda$ or $\beta$

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#4

$Old$ October 28th, 2009, 11:31 AM

statmajor $statmajor is offline$

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Quote:

Originally Posted by matheagle $View Post$

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)

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$Old$ October 28th, 2009, 12:03 PM

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They are the same, $\lambda=1/\beta$ use whatever your book is using.

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$Old$ October 28th, 2009, 12:04 PM

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That clears that up. Thanks.

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