# Find a general formula for the MLE for p

• ianrice
In summary, the Maximum Likelihood Estimation (MLE) for a parameter p is calculated by taking the derivative of the likelihood function with respect to p, setting it equal to 0, and solving for p. This method is used to estimate the most likely value of p that generated the observed data, and can be used with any type of data that follows a probability distribution. However, there are some assumptions and limitations when using the MLE, such as independent and identically distributed data and a correctly specified probability distribution. Additionally, it may not work well for small sample sizes or biased data.
ianrice
An experiment consists of giving a sequences of patients a risky treatment until two have died, and then recording N, the number who survived. If p is the proportion killed by the treatment, then the distribution of N is:

P(N=n)=((n+1)(1-p)^n)p^2

Find a general formula for the MLE for p:

The experiment is done in 8 hospitals, and the observed values of N are 3, 0, 4, 2, 3, 5, 1,3. Compute the estimate for p derived in part (a)

This looks like a homework question or a risky experiment. If it's homework, it should be posted in a different section of the forum along with a statement of your attempts. If this was a risky experiment, please describe all the details.

As Stephen said, questions of this nature must be posted in the Homework & Coursework sections, not in the technical math sections. I am closing this thread. You are welcome to repost in the HW & CW sections.

## What is a general formula for the MLE for p?

The general formula for the Maximum Likelihood Estimation (MLE) for a parameter p is:

MLE = argmaxp L(p)

where L(p) is the likelihood function, which is the probability of obtaining the observed data given a specific value of p. The MLE is the value of p that maximizes the likelihood function, or in other words, makes the observed data most probable.

## How is the MLE for p calculated?

The MLE for p is calculated by taking the derivative of the likelihood function with respect to p, setting it equal to 0, and solving for p. This value of p will be the one that maximizes the likelihood function and thus, is the MLE for p.

## What is the purpose of finding the MLE for p?

The purpose of finding the MLE for p is to estimate the most likely value of the parameter p that generated the observed data. This is important in statistical analysis as it allows us to make inferences about the underlying population based on the observed data.

## Can the MLE for p be used for any type of data?

Yes, the MLE for p can be used for any type of data, as long as the data follows a probability distribution that can be described by a likelihood function. The MLE method is a commonly used technique in statistical analysis for estimating parameters.

## Are there any assumptions or limitations when using the MLE for p?

Yes, there are some assumptions and limitations when using the MLE for p. Some of the common assumptions include: independent and identically distributed data, a correctly specified probability distribution, and a large enough sample size. Additionally, the MLE method may not always provide a unique solution and may not work well for small sample sizes or biased data.

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