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Unformatted text preview: ORIE 3500/5500 – Engineering Probability and Statistics II Fall 2010 Assignment 11 Problem 1 The bivariate normal distribution is frequently used to describe scores made on national standardized tests, like SAT. For con- creteness assume that a particular test has two parts, labeled “verbal” and “mathematics”. Furthermore, assume that a randomly selected student who takes this test will score X 1 and X 2 on these two parts, and that ( X 1 ,X 2 ) are bivariate normal, with the means μ 1 = 545, μ 2 = 555, σ 1 = 110, σ 2 = 120 and ρ = . 5. ( a ) Compute P ( | X 1- X 2 | > 5), the probability that the difference between the higher the lower score exceeds 5. ( b ) Compute the conditional versions of the probability in ( a ): P ( | X 1- X 2 | > 5 | X 1 = 550) and ( | X 1- X 2 | > 5 | X 2 = 550), i.e. the conditional probabilities that for a randomly selected student the difference between the two scores exceeds 5 points given that he/she scores 550 on one or another part of the test.scores 550 on one or another part of the test....
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This note was uploaded on 12/03/2010 for the course OR&IE 3500 taught by Professor Samorodnitsky during the Fall '10 term at Cornell.
- Fall '10