1. ## moments estimators

Let S=(1,2,3,4,5,6,7,8) be a random sample of independent values from a Binomial distribution B(250,P) with unknown p.
Find the moments estimator for p.
Some hints about that. or does 250 matters in this question ?

2. The method of moments estimator sets the sample mean equal to the population mean.
So, in a way you have two n's.
By the way, that data doesn't look like it would come from a Bin(250,p).

But what you should do is compute the sample mean of 1 through 8
which is (8)(9)/2=45 divided by 8 or 4.5 and set that equal to 250p and solve for p.

Thus $\displaystyle \hat P=4.5/250=.018$

This data is hardly from a bin(250,p) distribution.
Maybe more of a Poisson.

3. Originally Posted by matheagle
The method of moments estimator sets the sample mean equal to the population mean.
So, in a way you have two n's.
By the way, that data doesn't look like it would come from a Bin(250,p).

But what you should do is compute the sample mean of 1 through 8
which is (8)(9)/2=45 divided by 8 or 4.5 and set that equal to 250p and solve for p.

Thus $\displaystyle \hat P=4.5/250=.018$

This data is hardly from a bin(250,p) distribution.
Maybe more of a Poisson.
but is the estimator you find is biased or unbiased?

4. Originally Posted by fyw891105
but is the estimator you find is biased or unbiased?
Take an expected value and see for yourself The estimator is a nice, linear function of your sample: $\displaystyle \sum_{i = 1} ^ 8 \frac{S_i}{(8)(250)}$

5. I found this is biased because expectation rather than p is P/250.
Am I correct ?
thank you