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# Quiz4Aans - STAT 408 Spring 2009 Version A Name ANSWERS...

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STAT 408 Spring 2009 Version A Name ANSWERS . Section __________ Quiz 4 (10 points) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. Suppose that number of accidents at the Monstropolis power plant follows the Poisson process with the average rate of 0.40 accidents per week. Notations: X t = number of accidents in t weeks. T k = time of the k th accident. a) (3) Find the probability that the first accident would occur during the fourth week. T 1 has Exponential distribution with λ = 0.40 or θ = 1 / 0.4 = 2.5. P ( 3 < T 1 < 4 ) = - 4 3 4 . 0 4 . 0 dt t e = e 1.2 e 1.6 0.0993 . OR P ( 3 < T 1 < 4 ) = P ( T 1 > 3 ) – P ( T 1 > 4 ) = P ( X 3 = 0 ) – P ( X 4 = 0 ) = P ( Poisson ( 1.2 ) = 0 ) – P ( Poisson ( 1.6 ) = 0 ) = 0.301 – 0.202 = 0.099 . OR k fourth wee the during accident one least at weeks e first thre the during accidents no P AND = P ( X 3 = 0 ) × P ( X 1 1 ) = 0.301 × ( 1 – 0.670 ) 0.0993 . OR Week 1 Week 2 Week 3 Week 4 no accident no accident no accident accident(s) 0.670 × 0.670 × 0.670 × 0.330 0.0993 .

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b) (4) Find the probability that the third accident would occur during the fifth week.
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