Solution Found!
Let X be a binomial random variable with parameters (n,
Chapter 4, Problem 13TE(choose chapter or problem)
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.
Questions & Answers
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: