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? or
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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.
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 $\displaystyle \beta$
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)
They are the same, $\displaystyle \lambda=1/\beta$ use whatever your book is using.
That clears that up. Thanks.
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