Find the point estimate of p using method of moments

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SUMMARY

The point estimate of the probability of success, p, in a geometric distribution can be derived using the method of moments, where the sample mean, m, is utilized. Specifically, the relationship established is that p equals 1/m. This conclusion is drawn from the properties of the geometric distribution, where the mean is the reciprocal of the probability of success. Therefore, for a random sample of size n, the estimate for p is directly expressed in terms of the sample mean m.

PREREQUISITES
  • Understanding of geometric distribution and its properties
  • Familiarity with the method of moments in statistics
  • Knowledge of sample mean calculation
  • Basic statistical notation and terminology
NEXT STEPS
  • Study the derivation of the method of moments for various distributions
  • Learn about the properties and applications of geometric distributions
  • Explore advanced statistical estimation techniques beyond the method of moments
  • Review examples of point estimation in practical scenarios
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Students in statistics, data analysts, and anyone involved in statistical modeling or estimation techniques will benefit from this discussion.

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?
 

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