Lecture22 - GEM2900 Understanding Uncertainty Statistical...

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GEM2900: Understanding Uncertainty & Statistical Thinking DSAP, NUS, Semester 1, 2008/2009 – 1 GEM2900: Understanding Uncertainty & Statistical Thinking Berwin Turlach [email protected] Department of Statistics and Applied Probability National University of Singapore
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Poisson probability distribution (cont.) GEM2900: Understanding Uncertainty & Statistical Thinking DSAP, NUS, Semester 1, 2008/2009 – 166 E XAMPLE : (Death by Horse Kick in Prussian Army cont.) For this example: χ 2 = c summationdisplay i =1 ( o i - e i ) 2 e i = (109 - 108 . 67) 2 108 . 67 + (65 - 66 . 29) 2 66 . 29 + (22 - 20 . 22) 2 20 . 22 + (3 - 4 . 11) 2 4 . 11 + (1 - 0 . 71) 2 0 . 71 = 0 . 599929 But is this value “typical” or “suspiciously large”? It can be shown, that (under some conditions) this statistics follows an (approximate) χ 2 d distribution with a particular parameter d . Woolfson (2008, Chapters 6.2, 8 and 12.4)
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Joint distributions of (discrete) random variables GEM2900: Understanding Uncertainty & Statistical Thinking DSAP, NUS, Semester 1, 2008/2009 – 167 Let X and Y be two discrete random variables ( defined on the same probability space ( S , P ) ) .
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