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2. Let X1, X2, X3,..., Xn be a random sample from a U(0, 0) distribution. a) Find the maximum likelihood estimator of 0: b) Find the distribution function F of and deduce that the density function of is given by f(x) xn-1 On for 0≤x≤0. In = is an unbiased estimator of 0. c) Show that = n- n+1 n

2. Let X1, X2, X3,..., Xn be a random sample from a U(0, 0) distribution. a) Find the maximum likelihood estimator of 0: b) Find the distribution function F of and deduce that the density function of is given by f(x) xn-1 On for 0≤x≤0. In = is an unbiased estimator of 0. c) Show that = n- n+1 n

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 8SGR
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e) Suppose that n = 10 and that the following data values are ob- tained: 1.2 6.3 7.3 6.4 3.5 0.2 4.6 7.1 5.0 1.8 give a point estimate of 0.
Transcribed Image Text:e) Suppose that n = 10 and that the following data values are ob- tained: 1.2 6.3 7.3 6.4 3.5 0.2 4.6 7.1 5.0 1.8 give a point estimate of 0.
2. Let X₁, X2, X3,..., Xn be a random sample from a U (0,0) distribution. a) Find the maximum likelihood estimator of 0: b) Find the distribution function Fê of Ô and deduce that the density function of is given by fê (x) = n xn-1 оп for 0≤x≤0. c) Show that n+1 Tn = n is an unbiased estimator of 0. d) Determine the mean squared error of the point estimator Tn and deduce that Tn is a consistent estimator of 0.
Transcribed Image Text:2. Let X₁, X2, X3,..., Xn be a random sample from a U (0,0) distribution. a) Find the maximum likelihood estimator of 0: b) Find the distribution function Fê of Ô and deduce that the density function of is given by fê (x) = n xn-1 оп for 0≤x≤0. c) Show that n+1 Tn = n is an unbiased estimator of 0. d) Determine the mean squared error of the point estimator Tn and deduce that Tn is a consistent estimator of 0.
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