Let X have one of the following distributions: X H0 HA x1 .2 .1 x2 .3 .4 x3 .3 .1 x4 .2 .4 a. Com...
Let X have one of the following distributions:
X H0 HA
x1 .2 .1
x2 .3 .4
x3 .3 .1
x4 .2 .4
a. Compare the likelihood ratio, , for each possible value X and
order the xi
according to .
b. What is the likelihood ratio test of H0 versus HA at level α =
.2? What is the
test at level α = .5?
c. If the prior probabilities are P(H0) = P(HA), which outcomes
favor H0?
d. What prior probabilities correspond to the decision rules with α
= .2 and
α = .5?
Homework Answers
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Let X have one of the following distributions: X H0 HA x1 .2 .1 x2 .3 .4 x3 .3 .1 x4 .2 .4 a. Com...
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Suppose that X1, X2, . . . , Xn is an iid sample of N (0, σ2 ) observations, where σ 2 > 0 is unknown. Consider testing H0 : σ 2 = σ 2 0 versus H1 : σ 2 6= σ 2 0
Suppose that X1, X2, . . . , Xn is an iid sample of N (0, σ2
) observations, where σ
2 > 0 is
unknown. Consider testing
H0 : σ
2 = σ
2
0 versus H1 : σ
2
6= σ
2
0
;
where σ
2
0
is known.
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For the data x1 = -1, x2 =
-3, x3 = -2, x4 =
1, x5 = 0,
find ∑
(xi2).
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For the data x1 = -1, x2 =
-3, x3 = -2, x4 =
1, x5 = 0,
find ∑
(xi2).
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