# Exam 3 - December 2 2010 Math 351 Test 3 1 An urn has two...

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December 2, 2010 Math 351 - Test 3 1. An urn has two black and one white ball. An experiment consists of taking two balls from the urn. Call it “success” if both of them are black and call it “failure” if they are not both black. After you have chosen the two balls, put them back in the urn and then repeat. Let X be the number of trials to the ﬁrst success and let Y be the the number trials to the ﬁfth success. (a) Calculate p , the probability of success on any one trial. (b) What kind of random variable is X ? What kind of random variable is Y ? (c) What is the expected value of X ? (d) What is P { Y = 10 } ? 2. Consider a horizontal line segment of total length 15 inches. Fix a point P along the line segment at a distance 3 from the right side. Let X be a randomly chosen point along the line segment such that X is uniformly distributed. Let Y be the distance from X to P if X is to the right of P and let Y be 12 if X is to the left of P . Write down the expression (in terms

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## This note was uploaded on 03/05/2011 for the course MATH 351 taught by Professor Moumen,f during the Spring '08 term at George Mason.

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Exam 3 - December 2 2010 Math 351 Test 3 1 An urn has two...

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