HW4S - ISE 220 PROBABILITY CONCEPTS IN ENGINEERING...

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ISE 220 PROBABILITY CONCEPTS IN ENGINEERING Solutions to Homework Problem Set # 4 Instructor: Dr. Ashok Patel Fall 2010 Problem 1 ( 20 points ) D = sum of the arrival times is less than 30 minutes P ( D ) = Area(D)/Area(S) = (1/2) × (30) × (30) / 60 × 60 = 1/8. E = ratio of the arrival times X / Y is less than 2. P ( E ) = Area(E) / Area(S) = (1/2) × (60) × (30) / 60 × 60 = 1/4. Extra : F = multiplication of their arrival time is less than 100 P ( F ) = do it yourself .
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Problem 2 ( 30 points ) Note that S is uncountably infinite and its outcomes are uniformly distributed. So P ( A ) = S A of Area of Area = 2 2 1 1 4 / 1 2 × db da b = ( ) 4 1 4 / 1 1 2 + db b = 4 12 1 1 1 1 3 + b b = 24 13 . Problem 3 ( 30 points ) (i) P ( x < 1/2 | x + y ≥ 1/3 ) = [ ] } 3 / 1 { of Area } 3 / 1 { } 2 / 1 { of Area }) 3 / 1 ({ }) 3 / 1 { } 2 / 1 ({ + + < = + + < y x y x x y x P y x x P = do it yourself (ii) P
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HW4S - ISE 220 PROBABILITY CONCEPTS IN ENGINEERING...

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