For testing H0 : f(x) = begincases 2x; & 0 < x < 1 0; & otherwise endcases against H1 : f(x) = begincases 3x^2; & 0 < x < 1 0; & otherwise endcases on the basis of a single observation, the power of a most powerful test of size alpha = 0cdot 19 is:

Q13Section I (Objective (Q1–Q80))13 of 80

Statistical Inference — power of MP test for single observation

For testing $H_0 : f(x) = \begin{cases} 2x; & 0 < x < 1 \ 0; & \text{otherwise} \end{cases}$ against $H_1 : f(x) = \begin{cases} 3x^2; & 0 < x < 1 \ 0; & \text{otherwise} \end{cases}$ on the basis of a single observation, the power of a most powerful test of size $\alpha = 0\cdot 19$ is:

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