Homework10

# Homework10 - HOMEWORK PROBLEMS#10 SOLUTIONS TO EVEN...

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HOMEWORK PROBLEMS #10 SOLUTIONS TO EVEN PROBLEMS Chapter 4 74. Y N(78 , 6 2 ) (a) P ( Y > 72) = P ( Z > 72 - 78 6 ) = P ( Z > - 1) = 1 - . 1587 = . 8413. (b) P ± Z > y - 78 6 ² = 0 . 1, so y - 78 6 = 1 . 28 and y = 85 . 68. (c) P ± Z > y - 78 6 ² = 0 . 281, so y - 78 6 = 0 . 58 and y = 81 . 48. (d) P ± Z < y - 78 6 ² = 0 . 25, so y - 78 6 = - 0 . 675 and y = 73 . 95. We want P ( Y > 73 . 95 + 5) = P ( Z > 78 . 95 - 78 6 ) = P ( Z > . 16) = . 4364. (f) P ( Y > 84 | Y > 72) = P ( Y > 84) P ( Y > 72) = P ( Z > 84 - 78 6 ) . 8413 = P ( Z > 1) . 8413 = . 1587 . 8413 = . 1886. 124. (a) P ( PY > 0 . 4) = Z 1 . 4 12 y 2 (1 - y ) dy = 4 y 3 - 3 y 4 ³ ³ 1 . 4 = (4 - 3) - (4( . 4) 3 - 3( . 4) 4 ) = . 8208. 136. (a) m ( t ) = E ( e tY ) = Z 0 e ty ´ 1 θ µ e - y/θ dy = ´ 1 θ µZ 0 e - (1 - t ) y dy = ´ 1 θ µ - 1 1 θ - t ! e - (1 - t ) y ³ ³ ³ 0 = 1 1 - θt for t < 1 θ . (b) Since m 0 ( t ) = θ (1 - θt ) 2 and m 00 ( t ) = 2 θ 2 (1 - θt ) 3 , we have that E ( Y ) = m 0 (0) = θ and Var( Y ) = m 00 (0) - [ m 0 (0)] 2 = 2 θ 2 - θ 2 = θ 2 . 139.

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Homework10 - HOMEWORK PROBLEMS#10 SOLUTIONS TO EVEN...

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