suppose that a random variable X has a geometric distribution (pq^x) for which the parameter p is unknown (0<p<1). Find a statistic that will be an unbiased estimator of 1/p

Any help on this would be greatly appreciated, thank you so much

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- Mar 15th 2011, 10:35 PMholly123unbiased estimators
suppose that a random variable X has a geometric distribution (pq^x) for which the parameter p is unknown (0<p<1). Find a statistic that will be an unbiased estimator of 1/p

Any help on this would be greatly appreciated, thank you so much - Mar 15th 2011, 10:38 PMmatheagle
Do you have a sample or just one observation?

You do realize E(X)=1/p depending on how you define your distribution

http://en.wikipedia.org/wiki/Geometric_distribution

IN your case E(X)=(1/p)-1

So, in that setting X+1 is the answer - Mar 15th 2011, 10:44 PMholly123
Is there a way to prove X+1 is an unbiased estimator of 1/p? We usually write out proofs which I have not gotten the hang of yet

- Mar 15th 2011, 10:46 PMmatheagle
IF you are using $\displaystyle P(X=x)=pq^x$ for x=0,1,2,3...

Then E(X)=(1/p)-1, do you need a proof of that?

THEN E(X+1)=E(X)+1=(1/p)-1+1=1/p. - Mar 15th 2011, 11:04 PMmatheagle
OR for $\displaystyle P(X=x)=pq^{x-1}$ for x=1,2,3...

then E(X)=1/p. IN that case X is the answer

But do you have a sample X_1, X_2,....? or just one X? - Mar 16th 2011, 06:55 AMholly123
i think it is a sample

- Mar 16th 2011, 07:10 AMmatheagle
Then use $\displaystyle \bar X+1$