Question

Let X1, X2, Xn be a random sample from a population with a specific density function. What is the Maximum Likelihood Estimator (M.L.E) of a parameter in the density function, and how is it calculated?

Answer 1

The Maximum Likelihood Estimator (M.L.E) is a method used to estimate the parameter in the density function of a population based on a random sample. It involves maximizing the likelihood of observing the given sample. The M.L.E is calculated by taking the derivative of the likelihood function and solving for the parameter.

Step-by-step explanation:

The Maximum Likelihood Estimator (M.L.E) is a method used to estimate the parameter in the density function of a population based on a random sample. It aims to find the value of the parameter that maximizes the likelihood of observing the given sample. The M.L.E is calculated by taking the derivative of the likelihood function with respect to the parameter, setting it equal to zero, and solving for the parameter.