Practice_problems_1_solutions.pdf

Practice_problems_1_solutions.pdf - Part A 1 True 2 False 3...

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Part A 1. True 2. False 3. False 4. False 5. False 6. True 7. True Part B 1. (a) E ( Y ) = integraldisplay 12 6 yf ( y ) dy = integraldisplay 12 6 1 18 ( y 2 6 y ) dy = 1 18 bracketleftbigg y 3 3 3 y 2 bracketrightbiggvextendsingle vextendsingle vextendsingle vextendsingle 12 6 = 1 18 bracketleftbigg 1728 3 3 × 144 216 3 + 3 × 36 bracketrightbigg = 180 18 = 10 V ( Y ) = E ( Y 2 ) E ( Y ) 2 E ( Y 2 ) = integraldisplay 12 6 y 2 f ( y ) dy = integraldisplay 12 6 1 18 ( y 3 6 y 2 ) dy = 1 18 bracketleftbigg y 4 4 2 y 3 bracketrightbiggvextendsingle vextendsingle vextendsingle vextendsingle 12 6 = 1 18 [5184 2 × 1728 324 + 432] = 1836 18 = 102 V ( Y ) = 102 10 2 = 102 100 = 2 (b) E (3 X 5 Y ) = 3 E ( X ) 5 E ( Y ) = 3(6) 5(10) = 32 V (3 X 5 Y ) = 9 V ( X ) 25 V ( Y ) = 9(10) 25(2) = 140 1 + +
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2. Let H = having a defective headlight Let M = having a faulty muffler P ( H M ) = 0 . 10 P ( H M C ) = 0 . 15 P ( M | H ) = P ( M H ) P ( H ) = P ( M H ) P ( M H ) + P ( M C H ) = 0 . 10 0 . 10 + 0 . 15 = 0 . 40 3. (a) X = # tires before the first that fails before the guaranteed distance X Geom ( p = 0 . 02) P ( X = 50) = (1 0 . 02) 49 × 0 . 02 = 0 . 007432 (b) Y
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