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Unformatted text preview: supported by data NUS/FOS/DSAP 12 GEM2900 Semester 1, 2009/1010 Binomial & Poisson Distribution Assume a random variable, X, follows a binomial distribution X~Bin (n,p) Where ‘n’ is large and ‘p’ is small For small values of x, we have P ( X = x ) ≈ P (Y = x ) x, where Y is a Poisson random variable with λ = np That is, we may use Poisson to approximate Binomial if ‘n’ is large and ‘p’ is small NUS/FOS/DSAP 13 GEM2900 Semester 1, 2009/1010 Binomial & Poisson Distribution Assume a random variable, X, follows a binomial distribution X~Bin (n,p) Where ‘n’ is large and ‘p’ is small For small values of x, we have P ( X = x ) ≈ P (Y = x ) x, where Y is a Poisson random variable with λ = np That is, we may use Poisson to approximate Binomial if ‘n’ is large and ‘p’ is small NUS/FOS/DSAP 14 GEM2900 Semester 1, 2009/1010 Binomial & Poisson Distribution Example: Genetics... Suppose we are interested in genetic vulnerability to the breast cancer. We would expect 1 in 1000 women aged 40~49 whose mother have had breast cancer will develop a new case of breast th cancer over the next year of life. What is the probability that we find none out of 1000 women of this age group whose mother have had breast cancer will develop breast cancer over next year in life? What is the probability that we find 1 out 1000? 2 out of 1000? NUS/FOS/DSAP 15 GEM2900 Semester 1, 2009/1010 Binomial & Poisson Distribution Example: Genetics... x Using binomial P(X P(X = x) Using Poisson approximation approximation P(Y = x) 0 0.368 1 0.370 0.368 2 NUS/FOS/DSAP 0.366 0.185 0.184 16...
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