This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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....
View
Full
Document
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
 SAMORODNITSKY

Click to edit the document details