Question: please see the screenshot, only 3.2 is needed PROBLEM # 3: Let X1, X2, X3 follow a multinomial distribution with parameters 13 and 71' 2

please see the screenshot, only 3.2 is needed

PROBLEM # 3: Let X1, X2, X3 follow a multinomial distribution with parameters 13 and 71' 2 (7mm, 1'73)- 3.1 Consider the scenario that 71-1 2 \"Kg 2 1 9, and ''3 2 l9, please describe the testing procedure for the most powerful test with the signicance level a: when we test H0 : a9 = 0.2 vs Ha : I9 = 0.4 (feel free to assume that n is large for your testing procedure). 3.2 Now to check the assumed structure, we let the Ho be 1n = GT2 = 16, and g = 9, and H; be that the H0 is incorrect. Please provide a test statistic and the corresponding testing procedure for a generalized likelihood ratio test with the signicance level a for this problem. Feel free to use the notation of X30!) as the 1 a quantile of the Chi-square distribution with the degree of freedom 9

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