# Test 3.pdf - Name Stat 131 Test 3 u2013 100 Points Show...

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Name ____________________________ 4/21/10 Stat 131 Test 3 – 100 Points Show all work. Do in pencil. Don’t round until your final answer. Show as many decimals as practical to clearly indicate your final answer. Circle or mark your final answer. If your answer is a function, also list the valid values the variables take on. 1 otherwise. , 0 1 0 , 1 0 for , ) , ( y x y x y x f a Calculate P(0 ≤ X ≤0.5, 0.25 ≤ Y ≤ 1) (8 points) b Determine f ( x | y ) (8 points)
c Calculate ] 5 . 0 | 5 . 0 [ P Y X (8 points) 2 otherwise , 0 2 0 , 2 0 for , 8 1 ) , ( y x xy y x f E[X] = E[Y] = 6 7 a Calculate Cov[X, Y]. (8 points)
b Calculate Var[X] (this will also equal Var[Y]). (8 points) c Calculate Var[3X-2Y]. (8 points)
3 The lengths of life of two fuses are independent, each with density function otherwise. , 0 0 for , 7 ) ( 7 y e y y a Determine the joint density function (8 points) b The system that depends on these two fuses only needs one fuse to be working at a time. So, if the primary fuse blows, the secondary one kicks in. So, the total effective life of the system is 2 1 Y Y . Calculate ] 9 [ P 2 1 Y Y . (8 points) f
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