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b) Show that MsE(S²) = (п-1)* c) You are given another estimator of o? which is T² = = (X; – X)² i=1 2(n-1)o* For which MSE (T²)= Show that MSE (T²)< MSE(S²) when n2 n> 2.

b) Show that MsE(S²) = (п-1)* c) You are given another estimator of o? which is T² = = (X; – X)² i=1 2(n-1)o* For which MSE (T²)= Show that MSE (T²)< MSE(S²) when n2 n> 2.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...
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MATH 2275 Practice Sheet #1 1. Let X1, X2, ...,X, be a random sample of size n > 2 from a N(µ, o²)distribution. a) Show that S² = (X; – X)² п — 1 i=1 is an unbiased estimator of o?. 204 b) Show that MsE(S²) = (п-1)* c) You are given another estimator of o? which is 1 T2 = - =- (x; - X)² %3D i=1 2(n-1)o* For which MSE (T²)= Show that MSE (T²)< MSE(S²) when %3D n2 n> 2.
Transcribed Image Text:MATH 2275 Practice Sheet #1 1. Let X1, X2, ...,X, be a random sample of size n > 2 from a N(µ, o²)distribution. a) Show that S² = (X; – X)² п — 1 i=1 is an unbiased estimator of o?. 204 b) Show that MsE(S²) = (п-1)* c) You are given another estimator of o? which is 1 T2 = - =- (x; - X)² %3D i=1 2(n-1)o* For which MSE (T²)= Show that MSE (T²)< MSE(S²) when %3D n2 n> 2.
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