= 4. [12 marks] Let X = (X1, X2, ..., Xn) be a random sample from a normal distribution N(0, 8). a) [1 mark] Compute the

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4 12 Marks Let X X1 X2 Xn Be A Random Sample From A Normal Distribution N 0 8 A 1 Mark Compute The 1 (107.58 KiB) Viewed 25 times

= 4. [12 marks] Let X = (X1, X2, ..., Xn) be a random sample from a normal distribution N(0, 8). a) [1 mark] Compute the likelihood function for this sample. b) [2 marks] Find a complete and minimal sufficient statistic for this family. c) [3 marks] From the definition of monotone likelihood ratio, show that this family has a monotone likelihood ratio in its complete and sufficient statistic. d) [2 marks] Provide the structure of the UMP a-test for testing Ho: 0 > 10 versus H1 : 0 < 10 giving appropriate justification. e) [4 marks] Find the sample size n with power function y(@) so that approximately 7(8) = 0.95 and 7(10) = 0.05. Hint: The distribution of 21-1 Xi is normal with mean On and variance 8n and the upper 0.05 percentile of a standard normal is 1.65. : n