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PSTAT 120C:
Assignment # 1
Due April 13, 2006
These problems are due at the start of lecture on Thursday.
1. Show that if
T
is a suﬃcient statistic for estimating
θ
from the data
X
1
, . . . , X
n
then the
Generalized Likelihood Ratio Test (GLRT) statistic for testing
H
0
:
θ
∈
Ω
0
versus
H
a
:
θ
6∈
Ω
0
is a function of
T
. (Hint: use the factorization theorem.)
2. Suppose that
X
is a binomial random variable from
n
trials with probability
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Unformatted text preview: p . We want to test H : p = 1 2 versus H a : p 6 = 1 2 . (a) Find Î» , the GLRT statistic. (b) Argue that the critical region from the GLRT is of the same form as Â± Â± Â± Xn 2 Â± Â± Â± â‰¥ k Î± 3. Exercise 10.93 on page 523 in the textbook. 4. Exercises 8.81 and 8.87 on pages 409â€“410 in the textbook. 5. Exercise 10.67 on pages 505â€“506 in the textbook. 1...
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This note was uploaded on 04/09/2008 for the course PSTAT 120c taught by Professor Idk during the Spring '07 term at UCSB.
 Spring '07
 idk

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