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3. [10 + 5 points] Suppose the random variable X has the density 109(33) : 6exp(t93:) for :1: > 0 and the density is zero

3. [10 + 5 points] Suppose the random variable X has the density 109(33) : 6exp(t93:) for :1: > 0 and the density is zero otherwise. Suppose we wish to test H0:6:1vs.HA:6:91, where 61 is larger than 1. (a) Find the decision rule for the uniformly most powerful (UMP) test for testing H0 against HA at 5% level. (b) What is the power of this test when 61 : 2

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