Maximum Likelihood Estimation
Not what you're looking for?
Let the random samples x1, x2, x3,... xn drawn from normal distribution with known mean zero
a. Construct the likelihood function
b. Find the Nature Log of the likelihood function
c. Find the best estimate of the variance by MLE
d. What is the relationship between this estimate and the second moment <x²>
e. If we use second moment <x²> to estimate the variance, is the estimation biased? Why?
f. Under conditional (e) can this estimate be used to estimate population variance without bias? Why?
Purchase this Solution
Solution Summary
In this solution the maximum likelihood estimate of the variance of a normal distribution with mean zero is derived. It has been shown that this estimate is an unbiased estimate
Solution Preview
Let the random samples x1, x2, x3,... xn drawn from normal distribution with known mean μ which is equal to 0 and unknown variance φ.
F(x,φ)=[1√2П φ] exp [-(x- μ)²/(2 φ)]
a. Construct the likelihood function L(x, φ)
b. Find the Nature Log of the likelihood function ln L(x, φ)
c. Find the best ...
Purchase this Solution
Free BrainMass Quizzes
Measures of Central Tendency
This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.
Terms and Definitions for Statistics
This quiz covers basic terms and definitions of statistics.
Measures of Central Tendency
Tests knowledge of the three main measures of central tendency, including some simple calculation questions.
Know Your Statistical Concepts
Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.