 # 1. Suppose that 21 45 , ,..., XXX are independent, Xi Poisson �...

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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 :  20 vs H1 :  20 if 18 4.  ˆ MLE  . 2. Suppose that 21 72 , ,..., XXX are independent, i BetaX   ),1(~ . Find the p-value given by the likelihood ratio test of 4: H0   vs 4: H1   if 5.4 ˆ  MLE  . 3. 21 35 , ,..., XXX are independent, ~ )(1 Xi lExponentia , and 21 40 , ,...,YYY are independent, ~ )( 2 Yi lExponentia . We observe X 16 2. and Y  20 1. . We use the likelihood ratio test of H : 10 18 , 2  18 vs : is false. HH 01 Find the p-value. 4. )1 ,(~ 2 NormalX 1   , )2 ,(~ 2 NormalY 2   , and )3 ,(~ 2 NormalZ 3   . X, Y, and Z are independent. We use the likelihood ratio test of H :  3210  0 vs : is false. HH 01 We observe .1 80 .2, 52 ZYX  .1, 62. Find the p-value. 5.  Beta   )2,2(~ . X  nBinomial  ),2(~| . Find xf )(x . Simplify algebraically. 6.  Beta   )2,1(~ . X  nBinomial  ),2(~| . Find the posterior mean and standard deviation if X = 2 is observed. 7.  Beta(~ 32 ,   23) and X |   is ( 20 pnBinomial  ), . Find P |5.0( X  16) . 8.  Beta(~ 10 ,   10) and X |   is ( 100 pnBinomial  ), . We are testing 5.0: H0  versus 5.0: H1  . Find   0 | XHP  60 . 9. Suppose f ,1)(   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)(   10 , what is the probability Ken wins 2 of the 3 games if he loses the 1st game?

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