STA3007_0506_t11_ssol

STA3007_0506_t11_ssol - t ∼ Poisson(0.8(8 Pr X t = 3 Pr X...

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STA 3007 Applied Probability 2005 Tutorial 11 Suggested Solution 1. Marked Poisson Processes i. No. of English emigrating to area A Poisson( μ ) μ = λpt = 10( 1 12 )(4) = 10 3 Prob. that no English in Feb = e - 10 3 ii. Let X 0 ( t ) and X 1 ( t ) be the Poisson process of high priority and low priority cus- tomers respectively, X 0 ( t ) Poisson(0.2(8)) X 1
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Unformatted text preview: ( t ) ∼ Poisson(0.8(8)) Pr { X ( t ) = 3 } Pr { X 1 ( t ) = 5 } = e-1 . 6 (1 . 6) 3 3! e-6 . 4 (6 . 4) 5 5! = 0 . 0205 2. Spatial Poisson Processes i. F D ( x ) = Pr { D ≤ x } = 1-Pr { D > x } = 1-Pr { No particles in circle of radius x } = 1-e-νπx 2 , x > 1...
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