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Homework04Solutions

# Homework04Solutions - CHEN 3010 Applied Data Analysis Fall...

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CHEN 3010 Applied Data Analysis Fall 2004 Homework 04 Solutions Problem 1 3-96. a) Let X denote the number of tremors in a 12 month period. Then, X is a Poisson random variable with λ = 6. = = = ! 10 6 ) 10 ( 10 6 e W P 0.0413 b) λ =2(6) = 12 for a two year period. Let Y denote the number of tremors in a two year period. = = = ! 18 12 ) 18 ( 18 12 e Y P 0.0255 c) λ = (1/12)6 = 0.5 for a one month period. Let W denote the number of tremors in a one-month period. = = = ! 0 5 . 0 ) 0 ( 0 5 . 0 e W P 0.6065 d) λ = (1/2)6 = 3 for a six month period. Let V denote the number of tremors in a six- month period. PV eeeeee () !! . . >= −≤ = +++++ = = −−−−−− 51 5 1 3 0 3 1 3 2 3 3 3 4 3 5 10 9161 0 0839 30 31 32 33 34 35 Problem 2 3-112. a) PX e d x e ee xx . . .. . 12 15 0 2 0 0409 02 12 15 12 15 24 3 << = = = = −− b) P(X > 5) = == × x 5 1 03679 . . . By independence of the intervals in a Poisson process, the answer is 0.3679 2 = 0.1353. Alternatively, the answer can also be found as P(X > 10) = e -2 = 0.1353. The probability does depend on whether or not the lengths of highway are consecutive.

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Homework04Solutions - CHEN 3010 Applied Data Analysis Fall...

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