Lec 14 - Approx for Binomial & Poisson

Lec 14 - Approx for Binomial & Poisson - Some...

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Some Useful Approximations Poisson If np<5 and p<.1 or p>.9 If np>5 or .1<p<.9 Approx with POISSON Approx with NORMAL Binomial Approx with NORMAL Approximate Binomial with Poisson Normal Approximate Poisson with Normal
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Approximate Binomial with Poisson if np<5 and p<.1 or p>.9 r.v. X = # defectives out of a sample of n X is Binomial with E(X)=np and V(X)=np(1-p) Approximate as follows X is approximately Poisson with E(X)=np and V(X)=np(1-p) 2
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Example: Approximate Binomial with Poisson if np<5 and p<.1 or p>.9 ex: Sample 50 from a population with p=.04. Find the probability that the number of defectives in the sample is less than or equal to 4. r.v. X Binomial with N=50, p=.04 r.v. X approx Poisson with mean 2.0, P X x CP c x x x ( ) . . ( . ; ) . = 2245 = = = = - 4 50 04 96 2 0 4 947 0 4 50 μ where CP is the Cumulative Poisson Distribution with mean 2.0 and critical number 4 CP is easy to tabulate (only one parameter) 3
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Example: Approximate Binomial with Normal if np>5 or.1<p<.9 ex:
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