Section3.5-students_SP11

Section3.5-students_SP11 - rule: N-M distinct objects of...

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1 Finite Population of Size N Draw a random sample of size n : Two Schemes Sampling with Replacement Sampling without Replacement Population: Sample: 2 2 1 3 4 5 2 2 2 3 4 5 2 2 1 1 Never “remove” selected object from the population Each sample decreases population size by one unit Probability of S in each draw: Distribution: 1 Each element in the population has a label {0,1} [1 = yes, 0 = no] The Hypergeometric Distribution. .. ...is the exact probability model for the # of S ’s in a sample of size n when sampling without replacement . 1. Finite population of size N 2. Each individual is S (1) or F (0) and there are M total S ’s in population 3. A random sample of size n is taken without replacement X = # of S ’s in the sample is a Hypergeometric RV: 2 Section 3.5
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2 The Hypergeometric Distribution as product
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Unformatted text preview: rule: N-M distinct objects of type 2 ( , ) M distinct objects of type 1 Sample: n out of a total of N. pmf: 3 Section 3.5 The Negative Binomial Distribution. .. Binomial: Negative Binomial: 4 Section 3.5 3 The Negative Binomial Distribution. .. pmf: 1. Infinite population 2. Sequence of trials: each results in success (S) or failure (F) 3. Trials are independent and identical ( P(S)=p remains same) 4. Continue till you observe “ r” (fixed before hand) success X = # of failures observed till the termination is Negative Binomial RV ...is the exact probability model for the “# of failures” needed to observe a predetermined number of successes. 5 Section 3.5...
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Section3.5-students_SP11 - rule: N-M distinct objects of...

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