Find the point estimate of p using method of moments

Phox
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Homework Statement



Let X1, X2,..., Xn be a random sample of size n from a geometric distribution for which p is the probability of success. Let m denote the sample mean.

Use the method of moments to find a point estimate for p. Please write your answer in terms of m.

Homework Equations


The Attempt at a Solution


so wouldn't this just be the answer?

5ob18m.png


I don't understand what it means by in terms of m. It seems like the answer should be more simple than this because I have to type it into a basic text box.
 
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Phox said:

Homework Statement



Let X1, X2,..., Xn be a random sample of size n from a geometric distribution for which p is the probability of success. Let m denote the sample mean.

Use the method of moments to find a point estimate for p. Please write your answer in terms of m.

Homework Equations





The Attempt at a Solution


so wouldn't this just be the answer?

5ob18m.png


I don't understand what it means by in terms of m. It seems like the answer should be more simple than this because I have to type it into a basic text box.

What do you mean by ##k_1, k_2, \ldots, k_n?## For a given sample, how would you compute m?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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