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Lecture15_updated

# Lecture15_updated - any given week is a constant p Then the...

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Lecture 15 6 th June 2011

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Negative Binomial distribution: X: the number of FAILURES before the k th success. X~NB(k, p) Assumptions:
Exercise 5.5.2: You can get a group rate on tickets to play if you can find 25 people to go. Assume each person you ask responds independently and has a 20% chance of agreeing to buy a ticket. Let X be the total number of people you have to ask in order to find 25 who agree to buy a ticket. Find the probability function of X.

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Geometric distribution: Physical setup: Again we have independent Bernoulli trials, each having two possible outcomes (Success vs. Failure). The probability, p, of success is the same each time. However now X represents the number of failures before the FIRST success (i.e a negative binomial with k=1)
Examples: The probability you win a lottery prize in

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Unformatted text preview: any given week is a constant p. Then the number of weeks BEFORE you win a prize for the first time is a geometric distribution. • Fruit flies have either white or red eyes. Where the probability of white eyes is constant and equals 0.25. Then the number of flies that need to be checked BEFORE the first white eye is observed is a geometric distribution. • In summary we notice that the binomial, negative binomial and geometric models all assume: 1.Two outcomes in each trial, 2.Independent Trails, 3.Each trial has the same probability of success. • Example: Suppose there is a 30% chance of a car from a certain production line having a leaky windshield. The probability an inspector will have to check at least n cars to find the first one with a leaky windshield is 0.05. Find n....
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Lecture15_updated - any given week is a constant p Then the...

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