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Homework5

# Homework5 - HOMEWORK PROBLEMS#5 SOLUTIONS TO EVEN PROBLEMS...

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HOMEWORK PROBLEMS #5 SOLUTIONS TO EVEN PROBLEMS 38. Y Bin ( 4 , 1 3 ) (a) p ( y ) = 4 y ( 1 3 ) y ( 2 3 ) 4 - y (b) P ( Y 3) = P ( Y = 3) + P ( Y = 4) = 4 3 ( 1 3 ) 3 ( 2 3 ) + 4 4 ( 1 3 ) 4 = 8 81 + 1 81 = 1 9 0 . 11 (c) E ( Y ) = 4 × 1 3 = 4 3 1 . 33 (d) Var( Y ) = 4 × 1 3 × 2 3 = 8 9 0 . 89 52. Y Bin(20 , 0 . 7). Using the table on the back of the book we get: (a) P ( Y 17) = 1 - P ( Y 16) = 1 - 0 . 893 = 0 . 107 (b) P ( Y < 15) = P ( Y 14) = 0 . 584 60. Y Bin(20 , 0 . 8). Using the table on the back of the book we get: (a) P ( Y = 14) = P ( Y 14) - P ( Y 13) = 0 . 196 - 0 . 087 = 0 . 109 (b) P ( Y 10) = 1 - P ( Y 9) = 1 - 0 . 001 = 0 . 999 (c) P ( Y 16) = 0 . 589 (d) E ( Y ) = 20 × 0 . 8 = 16 and Var( Y ) = 20 × 0 . 8 × 0 . 2 = 3 . 2 (e) P (14 Y 18) = P ( Y 18) - P ( Y 13) = 0 . 931 - 0 . 087 = 0 . 844 74. Y Geo(0 . 9). So E ( Y ) = 1 0 . 9 = 10 9
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