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Asked Dec 10, 2019
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X1, X2, ..., X, is a random sample from
f (x) = 0e-0x
x > 0
To test Ho : 0 =
Oo versus H, : 0 ± 00
(a) Derive the likelihood ratio, A
(b) Find –2 In(A) = 2 e(ô) – e(0)|
where l(0) is the log likelihood evaluated at 0.
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X1, X2, ..., X, is a random sample from f (x) = 0e-0x x > 0 To test Ho : 0 = Oo versus H, : 0 ± 00 (a) Derive the likelihood ratio, A (b) Find –2 In(A) = 2 e(ô) – e(0)| where l(0) is the log likelihood evaluated at 0.

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Step 1

(a)

From the given information,

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Null Hypothesis: H, :0=0,. (=@,) Alternative Hypothesis: H, :0 + 0,

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Step 2

The density function is,

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f(x)= 0e*,x> 0. ',x>0.

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Step 3
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Ө, The likelihood ration is 1 = eZ*(6-4) and it is calculated below:

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