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1. Let be a sample from a Bernoulli distribution with parameter p.

a. Derive the method of moments estimator of p.

b. Verify if your method of moments estimator of p is unbiased for p.

2. Let be a sample from a Gamma distribution with parameter and .

a. If is known, derive the method of moments estimator of .

b. Verify if your method of moments estimator of is unbiased for .

First read these threads:

http://www.mathhelpforum.com/math-he...tion-help.html (posts #1, #2)

http://www.mathhelpforum.com/math-he...tatistics.html (posts #1, #2)

http://www.mathhelpforum.com/math-he...estimator.html

http://www.mathhelpforum.com/math-he...estimator.html

http://www.mathhelpforum.com/math-he...estimator.html

1. a. .

Sample mean .

So use as the estimator.

1. b. Show whether or not .

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2. a. .

Sample mean .

So use as the estimator.

2. b. Show whether or not .