# set6solutions - IE 300 GE 331 Discussion Problem Set 6 4-88...

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IE 300 / GE 331 Discussion Problem Set 6 4-88 Let X denote the distance between two consecutive major cracks. X is exponential with 0.2 cracks/mile. a) 10 2 ( 10) 0.1353 P X e e  b) Let Y denote the number of cracks in 10 miles. Y has a Poisson distribution with intensity 2 cracks per 10 miles. 22 ( 2) 2 / 2! 0.2707 P Y e c) The standard deviation of X is 1/ 5 miles. d) 12 15 (12 15) (15) (12) 0.0409 P X F F e e  e) 5 ( 5) 0.3679 P X e . Cracks occur in non-overlapping intervals independently. The required probability is thus 0 3679 0 1353 2 . . . f) By the memoryless property, the required conditional probability is equal to the unconditional probability ° ? > 10 ± = 0.1353 from a). 5-2 3 ,1 ( , ) (2 3 4 3 4 5 4 5 6) 1 xy f x y c         , c = 1/36 . a) 1 36 ( 1, 4) (1,1) (1,2) (1,3) (2 3 4) 1/ 4 P X Y f f f   b) ° ? = 1 ± = 1/4 is the same as part a).

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set6solutions - IE 300 GE 331 Discussion Problem Set 6 4-88...

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