1. Consider a distribution with density 0.71 (=;0) = { * - 0 <3 <1 else 0 (a) Based on a random sample of size n = 1, fi

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1 Consider A Distribution With Density 0 71 0 0 3 1 Else 0 A Based On A Random Sample Of Size N 1 Fi 1 (35.22 KiB) Viewed 17 times

1. Consider a distribution with density 0.71 (=;0) = { * - 0 <3 <1 else 0 (a) Based on a random sample of size n = 1, find the most powerful test of Ho : 0= 1 against H, : 0= 2 with a = 0.05. (b) Compute the power of the test from (a) for the alternative 0 = 2. (c) Suppose we observe r = 0.8. Find the p-value of this test. (d) Derive the most powerful test for the hypotheses of (a) based on a random sample of size n. Make sure to explicitly state both your test statistic function and your rejection region.