Thread: Exponential Distribution Question

1. 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?

or

2. 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.

3. 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 $\displaystyle \beta$

4. 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)

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

6. That clears that up. Thanks.