Question:
Let π be a random variable having a probability density function
\(f(x; ΞΈ) =\begin{cases} (3-ΞΈ){x^2-ΞΈ} & \quad \text{if }0<x<1,\\ 0, & \quad Otherwise \end{cases}\)
where π β {0, 1}. For testing the null hypothesis π»0 : π=0 against π»1 : π=1, the power of the most powerful test, at the level of significance πΌ=0.125, equals
Let π be a random variable having a probability density function
\(f(x; ΞΈ) =\begin{cases} (3-ΞΈ){x^2-ΞΈ} & \quad \text{if }0<x<1,\\ 0, & \quad Otherwise \end{cases}\)
where π β {0, 1}. For testing the null hypothesis π»0 : π=0 against π»1 : π=1, the power of the most powerful test, at the level of significance πΌ=0.125, equals
\(f(x; ΞΈ) =\begin{cases} (3-ΞΈ){x^2-ΞΈ} & \quad \text{if }0<x<1,\\ 0, & \quad Otherwise \end{cases}\)
where π β {0, 1}. For testing the null hypothesis π»0 : π=0 against π»1 : π=1, the power of the most powerful test, at the level of significance πΌ=0.125, equals
Updated On: Oct 1, 2024
- 0.15
- 0.25
- 0.35
- 0.45
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The Correct Option is B
Solution and Explanation
The correct option is (B): 0.25
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