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[null,null,"Counting Pot-holes on the N1"]
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["Here a hungry Statistician gets distracted from the task at hand"]
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[null,null,null,null,null,null,null,"In this picture a statistician takes time-out"]
[null,null,null,null,null,null,null,"to recalculate the apparently low probability"]
[null,null,null,null,null,null,null," of losing one's car down a pot-hole"]

{"sheet":"Notes","index":1,"n_rows":43,"n_cols":2,"rows_kept":43,"cut":false,"hidden":false,"merged":[]}
[null,"Aims"]
[null,"The Poisson is a difficult distribution to teach because the natural examples are not that intuitive for first years"]
[null,"I'm not sure this distribution should be taught in first year, but the pot hole example is a good one "]
[]
[null,"Exercises"]
[1,"Change the stretch sampled from 1 km to 5 kms to 10 kms. Discuss the effect."]
[2,"Change the number of replications from 500 to 1000 to 5000. Discuss the effect."]
[3,"Print out the associated graphs."]
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[null,"The authorities want to survey the state of the roads in SA before the 2010 World Cup"]
[null,"A company does a survey and ascertains that in the approximately 1 000 kms they survey "]
[null,"there are 1000 pot holes"]
[null,"However, all the information about where the potholes are located gets lost!"]
[]
[null,"If we assume that the potholes are in fact randomly distributed across the 1000 kms, we can approximate the "]
[null,"probability of different numbers of potholes on a randomly selected piece of road"]
[null,"In particular, we can answer questions of the type:"]
[null,"If I select a random 1 km (or 5 km) piece of road what is the probability of"]
[null,"0, 1, 2 or 15 potholes occuring in that road"]
[]
[null,"The simulation works as follows:"]
[null,"We get the computer to randomly distribute the locations of the 1000 potholes over the 1000 kms of road."]
[null,"by randomly allocating distances betwwen 0 and 1 000kms"]
[null,"We then view (consider) a random piece of road, say a randomly selected 2km stretch"]
[null,"and count the number of potholes in that section"]
[null,"We then repeat the sampling process of repeatedly taking 2km lengths and counting the number of potholes in the length"]
[null,"We then have assessed the empirical distribution of the number of potholes in a randomly selected 2km length of road"]
[]
[null,"We see this distribution is asymmetrical with a long right-hand tail"]
[null,"the more we repeat the sampling process,  the closer the results will approximate a Poisson distribution"]

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[null,"Av. # potholes/sampled stretch","l = ",{"$f":"nMice*D3","v":3},null,null,"3. Print (preview first)",null,null,null,null,2,1071]
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