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# Poisson - is small p X k = e-Î k k â‰ˆ n k n-k p k(1-p n-k...

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Learning Objectives Recognizeand usethe probability mass functions of common discreterandom variables: Uniform Bernoulli Binomial Geometric Poisson

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Poisson Poisson RV X with parameter λ p X ( k ) = e - λ λ k k ! k = 0 ,1 , K ,
Example 0 0.05 0.1 0.15 0.2 0.25 0 1 2 3 4 5 6 7 8 9 10 k p(k) lambda=5 lambda=3 p X ( k ) = e - λ λ k k ! k = 0 ,1 , K ,

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Poisson & Binomial Poisson RV X with parameter λ =np approximates binomial RV with parameters n and p if n is largeand p

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Unformatted text preview: is small p X ( k ) = e-Î» k k ! â‰ˆ n ! k !( n-k )! p k (1-p ) n-k k = ,1 , K , Example â€¢ n = 200, p = 0.1 k Binomial Poisson 1 1.5678e-08 4.1223e-08 10 0.0045 0.0058 15 0.0501 0.0516 20 0.0936 0.0888 100 2.4051e-46 2.7997e-37 Exercises â€¢ Exercise #1 â€¢ Exercise #2 â€¢ Exercise #3 â€¢ Exercise #4 â€¢ Exercise #5...
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