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practice2 - STAT 400 Exam 2 Practice Problems 1 Heidi and...

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STAT 400 Exam 2 Practice Problems 1. Heidi and Alex have agreed to meet for lunch between noon (0:00 p.m.) and 1:00 p.m. Denote Heidi’s arrival time by X, Alex’s by Y, and suppose X and Y are independent with probability density functions f X ( x ) = ( 3 x 2 0 x 1 0 otherwise f Y ( y ) = ( 5 y 4 0 y 1 0 otherwise (a) Write down the joint p.d.f. of ( X,Y ). (b) Find the probability that Heidi arrives before Alex. 1

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that are checked is lost. Suppose that a frequent-ﬂying businesswoman will be checking 120 bags over the course of the next year. Using Poisson approximation to ﬁnd the probability that she will lose 2 or more pieces of luggage. 3. Suppose that commercial airplane crashes in a certain country occur at the rate of 2.5 per year. Assume that such crashes follow a Poisson process, (a) Starting from now, let X denotes the time until the next crash, what is the distribution of X ? Write down the p.d.f. of X . (b) What is the probability that the next crash will occur within three months?
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practice2 - STAT 400 Exam 2 Practice Problems 1 Heidi and...

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