MSci_609_continous_probability_distribut

MSci_609_continous_probability_distribut - 1/25/2011 1...

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1/25/2011 1 CONTINUOUS PROBABILITY DISTRIBUTIONS INSTRUCTOR: AMER OBEIDI 1 In a risk - management scenarios, management may fail to recognize those improbable events yet with huge harmful consequences. For instance, NASA has experienced two disasters: the Space Shuttle Challenger was destroyed over the Atlantic Ocean, off the coast of central Florida, United States at 11:39 a.m. EST on January 28, 1986; and the Space Shuttle Columbia disaster occurred on February 1, 2003. There has been a total of 120 space missions. Assume failures continue to occur at the same rate and consider the next 23 missions. - What is the probability of exactly two failures? - What is the probability of no failures? 2
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1/25/2011 2 The pet industry has undergone a surge in recent years, surpassing even the $20 billion a year toy industry. According to the U.S. News & Worlds Report, 60% of U.S. households live with one or more pets. If four U.S. households are selected at random without replacement, determine the (approximate) probability that the number living with one or more pets will be: -exactly three - at least three - at most three. 3 A different representation of a random property 4
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1/25/2011 3 In modeling the vehicle-dispatching decisions of an airport-based taxi, assume travel times of successive taxi trips to and from the terminal to be independent random variables, and assume the average mean trip time for a taxi service to be 20 minutes. - What is the probability that a particular trip will take more than 30 minutes? - Two taxis have just been dispatched. What is the probability that both will be gone for more than 30 minutes? That at least one of the taxis will return within 30 minutes? 5 A professor believes that if a class is allowed to work on an examination as long as desired, the times spent by the students would be approximately normal with mean 40 minutes and standard deviation 6 minutes. Approximately how long should be allotted for the examination if the professor wants almost all (say, 97.5%) of the class to finish. 6
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1/25/2011 4 A continuous random variable Y has the following three properties: Y takes on an uncountable number of values in an interval—finite or infinite (- , ). A probability density function f ( x ) can be used to describe the characteristics of probability distribution of a continuous random variable. The probability that Y equals any particular value is zero . 7 Histogram approximates a probability density function. 8
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1/25/2011 5 A probability density function (PDF) is a theoretical model used to describe the probability distribution of a continuous random variable using a mathematical formula. Shows all values, X = x , and frequencies, f ( x ). If F ( x ) is the cumulative distribution function for a continuous random variable, X , then the density function f ( x ) for X is 9 Definition 10
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1/25/2011 6 f ( x ) is NOT a probability It is a smooth curve.
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MSci_609_continous_probability_distribut - 1/25/2011 1...

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