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**Unformatted text preview: **STAT 400 Examples for 09/15/2011 Fall 2011 Poisson Distribution: X = the number of occurrences of a particular event in an interval of time or space. P( X = x ) = ! λ λ x x e- ⋅ , x = 0, 1, 2, 3, … . E( X ) = λ , Var( X ) = λ . Table III ( pp. 580 – 582 ) gives P( X ≤ x ) 1. Traffic accidents at a particular intersection follow Poisson distribution with an average rate of 1.4 per week. a) What is the probability that the next week is accident-free? 1 week ⇒ λ = 1.4. P ( X = 0 ) = ! 4 . 1 4 . 1 e- ⋅ ≈ 0.2466 . b) What is the probability that there will be exactly 3 accidents next week? 1 week ⇒ λ = 1.4. P ( X = 3 ) = ! 3 4 . 1 4 . 1 3 e- ⋅ ≈ 0.1128 . c) What is the probability that there will be at most 2 accidents next week? 1 week ⇒ λ = 1.4. P ( X ≤ 2 ) = P ( X = 0 ) + P ( X = 1 ) + P ( X = 2 ) = ! ! ! 2 4 . 1 1 4 . 1 4 . 1 4 . 1 2 4 . 1 1 4 . 1 e e e--- ⋅ ⋅ ⋅ + + ≈ 0.2466 + 0.3452 + 0.2417 = 0.8335 . d) What is the probability that there will be at least 2 accidents during the next...

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