iid 4. Let X1, ...,Xn Exp(a), the exponential distribution with failure rate 2. Show that the...

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iid 4. Let X1, ...,Xn Exp(a), the exponential distribution with failure rate 2. Show that the test which rejects the null hyp

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Answer 1

Answer #1

Solution:-

Its Exponential Distribution and the random variable is iid.

Suppose tht,

X exp)

W want to test the

Ho: Verses H1 = 2

f(x) = de lo

and Likelyhood Function is,

L= Пе-Аг 1=1

I=! PuP = 1

Threfore Likehood ratio is,

L1 LO 2e- n1 e-n-11-i

L1 LO 2e-Σ I;

Since,

TY Oy

Rejction rgion is,

I; <c

C VI n n

C k , k>0 (Fixd constant).

Therefore MP-test for testing Hypothesis,

Reject if C k .

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Answer 2

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