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GATE Mathematics 2014 Paper

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Question : 43

Total: 55

Suppose that X is a population random variable with probability density function f(x;θ)={

θxθ−1‌if 0<x<1

where θ is a parameter. In order to test the null hypothesis H0:θ=2, against the alternative hypothesis H1:θ=3, the following test is used: Reject the null hypothesis if X1≥

and accept otherwise, where X1 is a random sample of size 1 drawn from the above population. Then the power of the test is _____

0.88 to 0.90
0.87 to 0.89
0.86 to 0.88
0.85 to 0.87

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