f (x; 0) = e-(a-0) I10,00) (x) and let 00 be a fixed number in O = (-∞, ∞). Consider the one-sided test Ho : 0 <0 versus H1 : 0 > 0. Show that the likelihood ratio test which rejects Ho if X(1) > K is a UMP Pg=0(X(1) 2 K). level a test where a =

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Exercise
Suppose X1,..., Xn is a random sample
from a distribution with pdf
f(x; 0) = e¯(x-0) I[0.00) (x)
and let 00 be a fixed number in e = (-∞, ). Consider the
one-sided test Ho : 0 <0 versus H1 :0 > 0. Show that the
likelihood ratio test which rejects Ho if X(1) > K is a UMP
Pg=0(X(1) 2 K).
level a test where a =
Dr. Asieh Abtahi - Faculty of Mathematics and Statistics-
Islamic Azad University of Shiraz - iran
24
Transcribed Image Text:Exercise Suppose X1,..., Xn is a random sample from a distribution with pdf f(x; 0) = e¯(x-0) I[0.00) (x) and let 00 be a fixed number in e = (-∞, ). Consider the one-sided test Ho : 0 <0 versus H1 :0 > 0. Show that the likelihood ratio test which rejects Ho if X(1) > K is a UMP Pg=0(X(1) 2 K). level a test where a = Dr. Asieh Abtahi - Faculty of Mathematics and Statistics- Islamic Azad University of Shiraz - iran 24
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