ST371-StudentNotes4-OtherDiscrete

ST371-StudentNotes4-OtherDiscrete - ST 371 Note Outline 4...

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Page 1 of 9 ST 371 Note Outline 4: Other Famous Discrete Distributions Textbook: 3.5, 3.6 Motivating Example: We are interested in learning about a student-run club on campus, which has 20 members. In this club, 10 members are women and 10 members are men. Suppose we sample 4 members at random without replacement* and record X = {number of females}. What distribution does X follow? *Note: Sampling with replacement means that we select a person from the population, measure them, then put them back into the population before we select again. Sampling without replacement means that we do not put the person back into the population before we select again. What if the club had 20,000 members, half of which were females? Note: We can use the Binomial Dist ribution… o If the sample is (Rule of thumb: Population at least 10 times larger than the sample) o Or if we are sampling with replacement When sampling without replacement from a small population, we _______________ use the Binomial Distribution, instead use the ______________________________ Distribution
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Page 2 of 9 THE HYPERGEOMETRIC DISTRIBUTION Conditions for using the Hypergeometric Distribution: 1. The population is finite and consists of 2. There are 2 possible outcomes for each individual: success and failure; and there are 3. A sample of __________ individuals are If these conditions are met, then X = {the number of successes} is a hypergeometric rv. The distribution of X depends on three parameters: Hypergeometric PMF : Notation: Mean and Variance of X ~ Hyper( n,M,N ) : Notes: __________ is the proportion of successes in the population i.e. the probability of success. If we replace this term with __________ in the above formulas, then we get: which are the mean and variance of the ____________________ distribution.
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