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4.5.5. Let X₁, X2 be a random sample of size n = 2 from the distribution having pdf f(x; 0) = (1/0) e-x/0, 0 < x <∞, zero elsewhere. We reject Ho: 0 = 2 and accept H₁0 = 1 if the observed values of X1, X2, say x1, x2, are such that f(x1; 2) f(x2; 2) f(x₁; 1)f(x2; 1) = 1 2 Here Ω {0:01,2}. Find the significance level of the test and the power of the test when Ho is false.

4.5.5. Let X₁, X2 be a random sample of size n = 2 from the distribution having pdf f(x; 0) = (1/0) e-x/0, 0 < x <∞, zero elsewhere. We reject Ho: 0 = 2 and accept H₁0 = 1 if the observed values of X1, X2, say x1, x2, are such that f(x1; 2) f(x2; 2) f(x₁; 1)f(x2; 1) = 1 2 Here Ω {0:01,2}. Find the significance level of the test and the power of the test when Ho is false.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**4.5.5.** Let \( X_1, X_2 \) be a random sample of size \( n = 2 \) from the distribution having pdf \( f(x;\theta) = (1/\theta)e^{-x/\theta} \), \( 0 < x < \infty \), zero elsewhere. We reject \( H_0 : \theta = 2 \) and accept \( H_1 : \theta = 1 \) if the observed values of \( X_1, X_2 \), say \( x_1, x_2 \), are such that \[ \frac{f(x_1; 2)f(x_2; 2)}{f(x_1; 1)f(x_2; 1)} \leq \frac{1}{2}. \] Here \( \Omega = \{\theta : \theta = 1, 2\} \). Find the significance level of the test and the power of the test when \( H_0 \) is false.
Transcribed Image Text:**4.5.5.** Let \( X_1, X_2 \) be a random sample of size \( n = 2 \) from the distribution having pdf \( f(x;\theta) = (1/\theta)e^{-x/\theta} \), \( 0 < x < \infty \), zero elsewhere. We reject \( H_0 : \theta = 2 \) and accept \( H_1 : \theta = 1 \) if the observed values of \( X_1, X_2 \), say \( x_1, x_2 \), are such that \[ \frac{f(x_1; 2)f(x_2; 2)}{f(x_1; 1)f(x_2; 1)} \leq \frac{1}{2}. \] Here \( \Omega = \{\theta : \theta = 1, 2\} \). Find the significance level of the test and the power of the test when \( H_0 \) is false.
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