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Special Distributions

Special Distributions. Onur DOĞAN. The Bernoulli Distributions. The Binomial Distributions. ljhlj. Example 1. Suppose that a machine produce s defective item with probability 0,1. a) When we select 5 items, find the probability of 1 item being defective .

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Special Distributions

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  1. SpecialDistributions Onur DOĞAN

  2. The Bernoulli Distributions • .

  3. The Binomial Distributions • ljhlj

  4. Example 1 • Suppose that a machine produces defective item with probability 0,1. a) Whenwe select5 items, find the probability of 1 itembeing defective. b) Ifthe amount of daily production is 100, thenwhat's the expected defective item amount? c)What’s the variance of defective items of samples around the expected defective items.

  5. Example 2 • The probabilityof making a successful surgery for the doctos is %80. • Ifthat doctor make 3 surgeries in one month, find the probabilities for all possible results.

  6. Hypergeometric Distribution. • .

  7. Example 3

  8. Example 4 • Supposethat in productionlineforevery 20 products, 4 of themarerequiredto be reprocessed. a) Ifweselect 2 products, findtheprobability of one of thembeingreprocessed. b) Ifweselected 10 products, howmany of themshouldhavebeenexpectedtoenterreprocessing.

  9. PoissonDistributions • E(X)=Var(X)=

  10. Example 5 • Suppose that,in İzmir the number ofpowerblackouteventshas the Poisson distributionwithmean 2, for oneyear. a)Find the probability that there will be no power blackout in following year? b)Find the probability that there will be 2 power blackout in next 6 months? c)Find the probability thatthere will be 2 or more blackoutevents in following year?

  11. Example 6 Solution

  12. The Negative Binomial Distributions

  13. The Negative Binomial Distributions

  14. The Geometric Distributions

  15. Example 7 • In a production line, it wasfoundthat 200out of 1000 items were found defective. a)What’s the probability thatthe first defective item is observedwhiletestingthe4th item? b)How many itemsshould have been tested untilthe first defective item found? c)What’s the probability of the first defective item is not the first tested one?

  16. The Multinomial Distributions

  17. Example 8 • Suppose that there are 3 different brands; A,B and C. And we have observed the be purchase probabilities as follows; P(A)=0,40 P(B)=0,10 P(C)=0,50 Suppose that there are 10 customers, what’s the probability that 2 of them buys A, 5 of them buys B and 3 of them buys C.

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