PDB_Stat_100_Lecture_12_Printable

PDB_Stat_100_Lecture_12_Printable - STA 100 Lecture 12 Paul...

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STA 100 Lecture 12 Paul Baines Department of Statistics University of California, Davis January 31st, 2011
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Admin for the Day I Please pick up Midterm+old homeworks I Homework 3 posted, due Wednesday (5pm) I Typo: Q2(d) – Compare Mean/SD to Q1(d)+(e) NOT Q1(e)! I Typo: Q2(f) – Compare Max to Q1(c) NOT Q1(f)! I Typo: Q2(h+j) – Swapped rows/cols, 500 x 100, 1000 x 100 I Updated version now posted References for Today: Rosner, Ch 4.9-4.12, 5.1-5.4 (7th Ed.) References for Monday: Rosner, Ch 5.1-5.6 (7th Ed.)
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Applying to Data We have studied various properties of the Poisson distribution. Now lets start by looking at how we might use the Poisson distribution for real data. . . Note : When we write X Poisson (5) we mean that X has a Poisson distribution with mean 5. For example: Y Bin (10 , 0 . 5), means that Y has a Bino- mial distribution with n = 10 and p = 0 . 5. Read ‘(blank 1) (blank 2)’as ‘(blank 1) has a (blank 2) dis- tribution’.
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Cholera Example Example: The number of cases of Cholera in each household in an Indian village were recorded. The data look like this: > cholera house cholera_cases 1 1 2 2 3 1 4 1 ... etc . .. Count the number of households with no cases, 1 case etc. . .
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Cholera Data > table(cholera$cholera_cases) 0 1 2 3 4 35 32 16 6 1 0 1 2 3 4 Indian Cholera Cases Cases per household Frequency 0 5 10 15 20 25 30 35
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Cholera: Poisson? Let X i be the number of Cholera cases in house i . Then suppose X i Poisson ( λ ), with each house being independent. house cholera_cases 1 1 # Assumed ~ Pois(lambda) 2 2 # Assumed ~ Pois(lambda) 3 1 # Assumed ~ Pois(lambda) ... etc . .. In the homework you generate 100 observations from a Poisson with mean 5. This though, is real data assumed to come from a Poisson distribution with mean λ . We don’t know what λ is though!
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Estimating λ Q: How might we estimate λ ? A: The number of cases of Cholera in each household is Poisson with mean λ , and households are independent. What should the mean number of cases of Cholera for all households be? Just
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PDB_Stat_100_Lecture_12_Printable - STA 100 Lecture 12 Paul...

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