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Math Help - Hypothesis Testing

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    Hypothesis Testing

    Let X have a pdf of the form f(x; {\theta}) = {\theta}x^{\theta-1} where {\theta}\in\{\theta: \theta=1, 2\}.

    To test the simple hypothesis H_0:\theta=1 against the alternative simple hypothesis H_1:\theta=2, use a random sample X_1, X_2 of size n=2 and define the critical region to be C = \{(x_1, x_2): \frac{3}{4}  \leq x_1x_2 \}.

    Find the power function of the test.

    I hate to ask for help when I feel like I don't have much of anything to show for my own efforts, but I feel stuck.

    I know I need \gamma(\theta) = P_{\theta}[\frac{3}{4}  \leq x_1x_2] = 1 - P_{\theta}[x_1x_2 \leq \frac{3}{4}]

    I don't know how to set the limits of integration on the joint pdf to get the answer given in the back of the book:
    1-(\frac{3}{4})^\theta+\theta(\frac{3}{4})^{\theta}l  og({\frac{3}{4})}<br />
    Last edited by Zithuan; April 7th 2009 at 05:58 PM.
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