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04spfin - Math 431 Final Exam Room B130 2:45pm Mrton Balzs...

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Math 431 Final Exam Room B130, May 10, 2004, 2:45pm M´arton Bal´azs NAME: 1. (40 points) For the magicball team of Wonderland, 30 persons are chosen out of the several million citizens. In Wonderland, there are only 10 names, and each of these names is given to 1/10 part of the population. Use indicator variables to compute the expected number of di±erent names in the team. What assumptions are you making? Bonus Problem: (10 points) Compute the standard deviation of the number of di±erent names in the team.

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Let X and Y be the two coordinates of a point uniformly chosen in the triangle with vertices (0 , 0), (1 , 1) and ( - 1 , 1). (In other words: the point ( X, Y ) is uniformly chosen in the set { ( x, y ) : 0 y 1 , - y x y } .) Compute (a) (15 points) E ( X ), E ( Y ), (b) (15 points) the correlation of X and Y , (c) (15 points) the conditional expectations E ( X | Y = y ) and E ( Y | X = x ). If you solve this by integration, make sure you take into account the appropriate limits of the
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04spfin - Math 431 Final Exam Room B130 2:45pm Mrton Balzs...

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