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= 7.1.7. Let X1, X2,..., Xn denote a random sample from a distribution that is N(μ,0), 0 < 0 <∞o, where u is unknown. Let Y (X-X)2/n and let L[0,8(y)] = [0-6(y)]². If we consider decision functions of the form 8(y) = by, where b does not depend upon y, show that R(0, 8) = (0²/n²) [(n² - 1)6² -2n(n-1)b+n²]. Show that b = n/(n+1) yields a minimum risk decision function of this form. Note that nY/(n+1) is not an unbiased estimator of 0. With 8(y) ny/(n + 1) and 0<0<∞, determine max, R(0,8) if it exists. =

= 7.1.7. Let X1, X2,..., Xn denote a random sample from a distribution that is N(μ,0), 0 < 0 <∞o, where u is unknown. Let Y (X-X)2/n and let L[0,8(y)] = [0-6(y)]². If we consider decision functions of the form 8(y) = by, where b does not depend upon y, show that R(0, 8) = (0²/n²) [(n² - 1)6² -2n(n-1)b+n²]. Show that b = n/(n+1) yields a minimum risk decision function of this form. Note that nY/(n+1) is not an unbiased estimator of 0. With 8(y) ny/(n + 1) and 0<0<∞, determine max, R(0,8) if it exists. =

MATLAB: An Introduction with Applications
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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= 7.1.7. Let X1, X2,..., Xn denote a random sample from a distribution that is N(μ,0), 0 < 0 <∞o, where u is unknown. Let Y E(Xi-X)2/n and let L[0,8(y)] = [0-8(y)]². If we consider decision functions of the form 8(y) = by, where b does not depend upon y, show that R(0, 8) = (0²/n²) [(n² - 1)6² -2n(n-1)b+n²]. Show that b = n/(n+1) yields a minimum risk decision function of this form. Note that nY/(n+1) is not an unbiased estimator of 0. With 8(y) ny/(n+1) and 0<0<∞, determine max, R(0,8) if it exists. =
Transcribed Image Text:= 7.1.7. Let X1, X2,..., Xn denote a random sample from a distribution that is N(μ,0), 0 < 0 <∞o, where u is unknown. Let Y E(Xi-X)2/n and let L[0,8(y)] = [0-8(y)]². If we consider decision functions of the form 8(y) = by, where b does not depend upon y, show that R(0, 8) = (0²/n²) [(n² - 1)6² -2n(n-1)b+n²]. Show that b = n/(n+1) yields a minimum risk decision function of this form. Note that nY/(n+1) is not an unbiased estimator of 0. With 8(y) ny/(n+1) and 0<0<∞, determine max, R(0,8) if it exists. =
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