2. (Exercise 8.5.2 from edition 8 of the textbook) Let X₁, X2,..., X10 be a random sample of size 10 from a Poisson dist

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2 Exercise 8 5 2 From Edition 8 Of The Textbook Let X X2 X10 Be A Random Sample Of Size 10 From A Poisson Dist 1 (141.27 KiB) Viewed 37 times

2. (Exercise 8.5.2 from edition 8 of the textbook) Let X₁, X2,..., X10 be a random sample of size 10 from a Poisson distribution with parameter 0. Let L(0) be the joint pmf of X₁, X2,..., X10. It is desired to test Ho: 0= against H₁ : 0 = 1. (a). Show that L()/L(1) ≤ k is equivalent to y = [1 i ≥ c. (b). In order to make a = 0.05, show that Ho is rejected if y > 9 and, if y = 9, reject Ho with probability (using some auxiliary random experiment). (c). If the loss function is such that L(1½, ½) = L(1, 1) = 0 and L(1,1) = 1 and L(1, 1) = 2, show that the minimax procedure is to reject Ho if y> 6 and, if y = 6, reject Ho with probability 0.08 (using some auxiliary random experiment).