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?
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?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 13PPS
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Q1. Consider a random sample X1, X2, ....., X30 of size 30, drawn from a
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?
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