V2 Rocket Hits
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V2 Rocket Hits 576 0.25Km 2 areas of South London in a grid (24 by 24) 535 rockets were fired randomly into the grid = n P(a rocket hits a particular grid area) = 1/576 = 0.001736 = θ Expected number of rocket hits in a particular area = 535/576 = 0.92882 How many rockets will hit any particular area? 0,1,2,… could be anything up to 535. The 0.9288 is the λ for the Poisson distribution: exp(-λ)λ P(# hits) ,# hits 0,1,2,... #hits! #hits Adapted from Richard Isaac, The Pleasures of Probability, Springer Verlag, 1995, pp. 99- 101.
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V2 Rocket Hits. Adapted from Richard Isaac, The Pleasures of Probability, Springer Verlag, 1995, pp. 99-101. 576 0.25Km 2 areas of South London in a grid (24 by 24) 535 rockets were fired randomly into the grid = n P(a rocket hits a particular grid area) = 1/576 = 0.001736 = θ - PowerPoint PPT Presentation
Transcript of V2 Rocket Hits
V2 Rocket Hits
576 0.25Km2 areas of South London in a grid (24 by 24)535 rockets were fired randomly into the grid = nP(a rocket hits a particular grid area) = 1/576 = 0.001736 = θExpected number of rocket hits in a particular area = 535/576 = 0.92882How many rockets will hit any particular area? 0,1,2,… could be anything up to 535.The 0.9288 is the λ for the Poisson distribution:
exp(-λ)λP(#hits) ,#hits 0,1,2,...#hits!
#hits
Adapted from Richard Isaac, The Pleasures of Probability, Springer Verlag, 1995, pp. 99-101.
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Poisson Process• θ = 1/169• N = 133• λ = 133 * 1/169 = 0.787• Probabilities:
– P(X=0) = .4552– P(X=1) = .3582– P(X=2) = .1410– P(X=3) = .0370– P(X=4) = .0073– P(X>4) = .0013
Interpreting The Process
• λ = 0.787• Probabilities:
– P(X=0) = .4552– P(X=1) = .3582– P(X=2) = .1410– P(X=3) = .0370– P(X=4) = .0073– P(X>4) = .0013
• There are 169 squares• There are 133 “trials”• Expect .4552*169 = 76.6
to have 0 hits/square• Expect .3582*169 = 60.5
to have 1 hit/square• Etc.• Expect the average
number of hits/square to = .787.
Does the Theory Work?Theoretical Outcomes
Sample Outcomes
Outcome Probability Number of Cells
Sample Proportion Number of cells
0 .4552 77 .4733 801 .3582 60.5 .2781 472 1410 23.8 .1420 243 0370 6.3 .0592 104 0073 1.2 .0118 2
> 4 0013 0.2 .0000 0
n*λ = .787 0(80)+1(47)+2(24)+...]/169=.787
