Question: Let X1 X2 X3 be a random sample of size

Let X1, X2, X3 be a random sample of size n = 3 from an exponential distribution with mean θ > 0. Reject the simple null hypothesis H0: θ = 2, and accept the composite alternative hypothesis H1: θ < 2, if the observed sum 3i=1 xi ≤ 2.
(a) What is the power function K(θ), written as an integral?
(b) Using integration by parts, define the power function as a summation.
(c) With the help of Table III in Appendix B, determine α = K(2), K(1), K(1/2), and K(1/4).

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