Sampling Distribution

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NPWagner

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Nov 2, 2004
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Hey, i need help on this one.

Consider the probablity distribution shown here:

x 0 1 4
p(x) 1/3 1/3 1/3

A. Find the sampling distribution of the sample variance s^2 for a random sample of n=2 measurements from this distribution.
B. Show that s^2 is an unbiased estimator for σ^2.


Thanks!
 
NPWagner said:
x 0 1 4
p(x) 1/3 1/3 1/3

A. Find the sampling distribution of the sample variance s^2 for a random sample of n=2 measurements from this distribution.
B. Show that s^2 is an unbiased estimator for σ^2.
Click to expand...
The sampling distribution for the Mean is easy enough. With a sample size of two, there are only three possible outcomes. From this you can build the entire distribution. You can also do this with the sample variance.

Pick(0,1) -- Mean = 0.5 -- Pr = 1/3
Pick(0,4) -- Mean = 2.0 -- Pr = 1/3
Pick(1,4) -- Mean = 2.5 -- Pr = 1/3

OK, so what's the sample variance if you pick 0 and 1?
 
NPWagner said:
anyone? the HW is due tommorow and im still lost on this subject
Click to expand...
Sorry about that. Sometimes folks ask for stuff that is so foggy that I have to go find a book and read up on it. :cry:
 
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