# 04faex2a - Math 431 Second Evening Exam Version A Room B123...

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Version A Room B123, 5:00pm - 6:00pm, November 19, 2004 M´arton Bal´azs NAME: 1. Assume a reservoir of 10 000 gallons gets Flled every time a rainfall happens, and has 10 000 e - t/ 2 gallons of water t time after the last rainfall (where t is measured in weeks). Times passing between consecutive rainfalls are independent, and the time T between two rainfalls is an exponentially distributed random variable with parameter 1 2 (weeks - 1 ). (a) (30 points) Let X = 10 000 e - T/ 2 be the amount of water in the reservoir just when the next rainfall begins. Then X is a random variable. Compute its distribution function and density function. What kind of random variable is it? What is its expectation? (b) (30 points) What is the probability that there are no rainfalls in June (we can assume that June is precisely 4 weeks long)? What is the expected number of rainfalls in June? What is the probability that there are at least three rainfalls in June? 1

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## This note was uploaded on 08/11/2008 for the course MATH 431 taught by Professor Balazs during the Fall '05 term at University of Wisconsin.

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04faex2a - Math 431 Second Evening Exam Version A Room B123...

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