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Let X be a binomial random variable with parameters (n,

Chapter 4, Problem 13TE

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QUESTION:

Problem 13TE

Let X be a binomial random variable with parameters (n, p). What value of p maximizes P{X = k},k =0,1, ... , n? This is an example of a statistical method used to estimate p when a binomial (n, p) random variable is observed to equal k. If we assume that n is known, then we estimate pby choosing that value of p that maximizes P{X = k}. This is known as the method of maximum likelihood estimation.

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QUESTION:

Problem 13TE

Let X be a binomial random variable with parameters (n, p). What value of p maximizes P{X = k},k =0,1, ... , n? This is an example of a statistical method used to estimate p when a binomial (n, p) random variable is observed to equal k. If we assume that n is known, then we estimate pby choosing that value of p that maximizes P{X = k}. This is known as the method of maximum likelihood estimation.

ANSWER:

Solution 13TE

Step1 of 2:

Let us consider a random variable ‘X’ it follows a binomial distribution with parameters ‘n and p.’

We need to find the value of p maximizes P{X = k},k =0,1, ... , n.


Step2 of 2:

Here X follows a binomial distribution with parameters ‘n and p.’ the probability mass function of the binomial distribution is:

           

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