Let X 1 , , X n be i i d with the exponential distribution with parameter Suppose that we wish to test the hypotheses H 0 0 , H 1 0 Let Let c be the test that rejects H 0 if X c a Show that ( c ) is a decreasing function of b Find c in order to make c have size 0 c Let 0 2, n 1, and 0 0 1 Find the ...

The power function given above is sketched as below On OoW ...

Let X 1 , . . . , X n be i.i.d. with the exponential distribution with

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Let X₁, . . . , X_n be i.i.d. with the exponential distribution with parameter θ. Suppose that we wish to test the hypotheses

H₀ : θ ≥ θ₀,

H₁ : θ < θ₀.

Let . Let δ_c be the test that rejects H₀ if X ≥ c.

a. Show that π(θ|δ_c) is a decreasing function of θ.

b. Find c in order to make δ_c have size α₀.

c. Let θ₀ = 2, n = 1, and α₀ = 0.1. Find the precise form of the test δ_c and sketch its power function.

Related Book For answer-question

Probability and Statistics

ISBN: 978-0321500465

4th edition

Authors: Morris H. DeGroot, Mark J. Schervish

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Posted Date: Apr 12, 2021 05:46 AM

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Let X 1 , . . . , X n be i.i.d. with the exponential distribution with

Question:

X = E-1 Xi Ξ i=1 X = E-1 Xi Ξ i=1

Expert Answer:

The power function given above is sketched as below On OoW ... View the full answer

Probability and Statistics

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