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Power function

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Let X ~ B(1,theta) (f(x) = (theta^x)*(1-theta)^(1-x) x = 0,1). To test H_0 : theta=0.25 vs H_a : theta < 0.25, we take a random sample of size 10 and reject the H_0 if and only if Sigma(x_i)<1 (i.e. the sum of all x sub i with i ranging from 1 to 10 is less than 1). Find the power function pi(theta), 0 < theta <= 0.25, of this test.

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The solution contains the determination of the power function of a hypothesis.

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Let be the random sample taken from the population.
Since 's are random samples taken from , follows a Binomial distribution ...

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