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Summary_exam2

# Summary_exam2 - Special Discrete RVs Sect 3.4 Binomial RV 1...

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1 Special Discrete RV’s Sect 3.4: Binomial RV 1. Assumptions and definition i. Experiment consists of n repeated trials ii. There are only two possible outcomes on each trial: success (S) or failure (F). iii. Trials are independent iv. Prob. of success is p on each trial. Then X = the number of successes is a binomial RV. X ~ Bin( n,p ).

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2 2. pmf for x = 0, 1, …, n; 0 else 3. Facts If X ~ Bin( n, p ) and Y = number of failures, then Y ~ Bin( n , 1- p ) x n x p p x n p n x b x p ) 1 ( ) , ; ( ) ( ) 1 ( and 2 p np np
3 Sect. 3.5: Hypergeometric RV 1. Assumptions and definition: N objects of 2 types, success or failure . Assume M successes (N-M failures). Random sample of n objects, without replacement (means trials are dependent). X = number of successes is a hypergeo. RV. 2. pmf for x = 0, 1, …, n ; x < M ; and n - x < N M; 0 else n N x n M N x M , N) h(x ; n, M x p ) (

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4 3. Facts 4. Calculations: Calc or comp., but if N is large and n is small compared to N, approximate hypergeo. prob.s by binomial probs: When: text (p. 109) says n < .05 N Remark : If n is also large, we may approximate this binomial by a normal or a Poisson N M n 1 1 2 N n N N M N M n ) / , ( N M p n Bin X
5 Sect 3.5 Negative Binomial RV 1. Assumptions and definition : Experiment consists

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Summary_exam2 - Special Discrete RVs Sect 3.4 Binomial RV 1...

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