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HYPERGEOMETRIC DISTRIBUTION

HYPERGEOMETRIC DISTRIBUTION. PREPARED BY :A.TUĞBA GÖRE 2000432033. HYPERGEOMETRIC DISTRIBUTION. BASİC CHARACTERİSTİCS. It models that the total number of successes in a size sample drawn without replacement from a finite population.

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HYPERGEOMETRIC DISTRIBUTION

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  1. HYPERGEOMETRIC DISTRIBUTION PREPARED BY :A.TUĞBA GÖRE 2000432033

  2. HYPERGEOMETRIC DISTRIBUTION BASİC CHARACTERİSTİCS • It models that the total number of successes in a size sample drawn without replacement from a finite population. • It differs from the binomial only in that the population is finite and the sampling from the population is without replacement. • Trials are dependent

  3. HYPERGEOMETRIC DISTRIBUTION n= sample size A+B=population size A=successes in population X=number of successes in sample

  4. HYPERGEOMETRICDISTRIBUTION Mean , Variance and Standard Deviation

  5. If HYPERGEOMETRICDISTRIBUTION Binomial Approximation Requariments : If A+B=N and n≤0,05N , Binomial can be used instead of hypergeometric distribution Poisson Approximation Requariments: APPROXİMATİONS Poisson can be used instead of hypergeometric distribution

  6. HYPERGEOMETRICDISTRIBUTION Example 1 :A carton contains 24 light bulbs, three of which are defective. What is the probability that, if a sample of six is chosen at random from the carton of bulbs, x will be defective? That is no defective

  7. HYPERGEOMETRICDISTRIBUTION (example continued) That is 3 will be defective. Example 2:Suppose that 7 balls are selected at random without replacement from a box containing 5 red balls and 10 blue balls .If X denotes the proportion of red balls in the sample, what are the mean and the variance of X ?

  8. HYPERGEOMETRICDISTRIBUTION A=5 red B=10 blue A+B =15 n=7

  9. HYPERGEOMETRICDISTRIBUTION Example4:Suppose that a shipment contains 5 defective items and 10 non defective items .If 7 items are selected at random without replacement , what is the probability that at least 3 defective items will be obtained? N=15 (5 defective , 10 nondefective ) n=7

  10. HYPERGEOMETRICDISTRIBUTION Example 3 :If a random variable X has a hyper geometric distribution with parameters A=8 , B=20 and n, for what value of n will Var(x) be maximum ? n=28 or n=0 for variance to be maximum

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