Answered: Consider a random sample X1, X2, .....,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Q1. Consider a random sample X1, X2, ....., X30 of size 30, drawn from a
normal distribution with μ= 30, find maximum likelihood estimator of the
population variance σ2 .
a) Is the maximum likelihood estimator obtained in part (i) biased?
Justify your answer.
b) If the observed sample is 3, 6, 2, 0, 4, 3; compute the MLE of σ2
.
c) How would your answer in part (i) be affected if the number of
observations remains 30 and μ is reduced to zero?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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