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.

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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.
Transcribed Image Text: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.
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