Lecture21 - GEM2900: Understanding Uncertainty...

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Unformatted text preview: GEM2900: Understanding Uncertainty & Statistical Thinking DSAP, NUS, Semester 1, 2008/2009 – 1 GEM2900: Understanding Uncertainty & Statistical Thinking Berwin Turlach statba@nus.edu.sg Department of Statistics and Applied Probability National University of Singapore Poisson probability distribution GEM2900: Understanding Uncertainty & Statistical Thinking DSAP, NUS, Semester 1, 2008/2009 – 158 A random variable X has a Poisson distribution if its p.m.f. is P ( X = x ) = p X ( x ) = e- λ λ x x ! , x = 0 , 1 , 2 , . . . for some λ > . We also write X ∼ Poisson( λ ) . If X has a Poisson distribution with parameter λ , then E[ X ] = Var[ X ] = λ Woolfson (2008, Chapter 12) Poisson probability distribution (cont.) GEM2900: Understanding Uncertainty & Statistical Thinking DSAP, NUS, Semester 1, 2008/2009 – 159 E XAMPLE : Let X denote the number of flaws on the surface of a randomly selected boiler of a certain type. Suppose X has a Poisson distribution with λ = 5 . Then the probability that a randomly selected boiler has exactly two flaws is P ( X = 2) = e- 5 5 2 2! ≈ . 084 The probability that a boiler contains at most two flaws is P ( X ≤ 2) = 2 summationdisplay x =0 e- 5 5 x x !...
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Lecture21 - GEM2900: Understanding Uncertainty...

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