Find the point estimate of p using method of moments

In summary, to find a point estimate for p using the method of moments, you would use the sample mean, denoted by m, as your estimate. This is because the sample mean is equal to the expected value of a geometric distribution, which is p. Therefore, the point estimate for p would be m.
  • #1
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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  • #2
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?
 

FAQ: Find the point estimate of p using method of moments

What is the method of moments?

The method of moments is a statistical technique used to estimate the parameters of a population based on a set of sample data. It assumes that the population moments (such as mean, variance, etc.) can be approximated by the corresponding sample moments.

How is the point estimate of p calculated using the method of moments?

In order to calculate the point estimate of p using the method of moments, you need to first set the first moment (mean) of the population equal to the first moment of the sample. Then, solve for p using algebraic manipulation.

Is the point estimate of p always an accurate representation of the true population parameter?

No, the point estimate of p is not always an accurate representation of the true population parameter. It is based on a sample of data and is subject to sampling error. The larger the sample size, the more accurate the estimate is likely to be.

Are there any assumptions or limitations when using the method of moments to estimate p?

Yes, there are a few assumptions and limitations when using the method of moments. One major assumption is that the population follows a specific distribution (such as a normal or binomial distribution). Additionally, the method may not work well for small sample sizes or if the population has a high degree of variability.

How does the method of moments compare to other methods of estimating p?

The method of moments is just one of many methods used to estimate p. Other methods include maximum likelihood estimation and Bayesian estimation. The choice of method often depends on the specific characteristics of the data and the research question being addressed.

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