# Probability : Maximium Likelihood Estimator and p-Values

A GMAT test center reports that out of 200 students who took a GMAT test at the test center 60 scored above 600.

a) Derive the maximum likelihood estimator (MLE) of p, the proportion of students scoring above 600. What is the ML estimate of n*p(1-p)

b) What is the MLE of P(X<50)?

c) Test if the proportion of students scoring abve 600 is lower than 0.4 at the center at alpha = 0.01 using p-value.

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The Likelihood Function

Maximum likelihood estimation endeavors to find the most "likely" values of distribution parameters for a set of data by maximizing the value of what is called the "likelihood function." This likelihood function is largely based on the probability density function (pdf) for a given distribution. As an example, consider a generic pdf:

where x represents the data (times-to-failure) and k are the parameters to be estimated. For a ...

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Maximium Likelihood Estimator and p-Values are investigated. The solution is detailed and well presented.