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1. Suppose that 21 45 , ,..., XXX are independent, Xi Poisson  )(~ . Find the p-value given by the likelihood ratio test of H0 : ο€½ 20 vs H1 : ο‚Ή 20 if 18 4.  Λ† MLE ο€½ . 2. Suppose that 21 72 , ,..., XXX are independent, i BetaX ο€½ο€½  ),1(~ . Find the p-value given by the likelihood ratio test of 4: H0  ο€½ vs 4: H1  ο‚Ή if 5.4 Λ†  MLE ο€½ . 3. 21 35 , ,..., XXX are independent, ~ )(1 Xi lExponentia , and 21 40 , ,...,YYY are independent, ~ )( 2 Yi lExponentia . We observe X ο€½16 2. and Y ο€½ 20 1. . We use the likelihood ratio test of H : 10 18 , 2 ο€½ο€½ 18 vs : is false. HH 01 Find the p-value. 4. )1 ,(~ 2 NormalX 1  ο€½ο€½ , )2 ,(~ 2 NormalY 2  ο€½ο€½ , and )3 ,(~ 2 NormalZ 3  ο€½ο€½ . X, Y, and Z are independent. We use the likelihood ratio test of H :  3210 ο€½ο€½ο€½ 0 vs : is false. HH 01 We observe .1 80 .2, 52 ZYX ο€½ο€½ο€½ .1, 62. Find the p-value. 5.  Beta  ο€½ο€½ )2,2(~ . X  nBinomial ο€½ ),2(~| . Find xf )(x . Simplify algebraically. 6.  Beta  ο€½ο€½ )2,1(~ . X  nBinomial ο€½ ),2(~| . Find the posterior mean and standard deviation if X = 2 is observed. 7.  Beta(~ 32 ,  ο€½ο€½ 23) and X |   is ( 20 pnBinomial ο€½ο€½ ), . Find P |5.0( X  16) . 8.  Beta(~ 10 ,  ο€½ο€½ 10) and X |   is ( 100 pnBinomial ο€½ο€½ ), . We are testing 5.0: H0  versus 5.0: H1  . Find   0 | XHP ο€½ 60 . 9. Suppose f ,1)(  ο€Όο€Όο€½ 10 , X |  ~ Binomial(n = 3,  ), Y |  ~ Binomial(n = 2,  ). Give yf )( y if X = 0. Simplify your answer algebraically. 10. Ken is the best cribbage player at Hoover High. Gordon is the best cribbage player at Wilson High. They play a three game match. Ken has probability  of winning each game. If we take f  ,1)(  ο€Όο€Όο€½ 10 , what is the probability Ken wins 2 of the 3 games if he loses the 1st game?

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