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Suppose three tests are administered to a random sample of college students. Let X₁,..., Xy be observation vectors in R³ that list the three scores of each student, and for j = 1,2,3, let xj denote a student's score on the jth exam. Suppose the covariance matrix of the data is 80 84 36 S = 84 117 69 36 69 50 Let y = ₁x1 + ₂x2 + 3x3 be an "index" of student performance with c7 + c3 + c3 = 1 and c₁ ≥ 0. Find the constants C₁,C2,C3 so that the variance of y over the data set is as large as possible. Enter the values of c₁.c2.c3 into the answer box below, separated by comm ommas.

Suppose three tests are administered to a random sample of college students. Let X₁,..., Xy be observation vectors in R³ that list the three scores of each student, and for j = 1,2,3, let xj denote a student's score on the jth exam. Suppose the covariance matrix of the data is 80 84 36 S = 84 117 69 36 69 50 Let y = ₁x1 + ₂x2 + 3x3 be an "index" of student performance with c7 + c3 + c3 = 1 and c₁ ≥ 0. Find the constants C₁,C2,C3 so that the variance of y over the data set is as large as possible. Enter the values of c₁.c2.c3 into the answer box below, separated by comm ommas.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose three tests are administered to a random sample of college students. Let X₁,...,Xy be observation vectors in R³ that list the three scores of each student, and for j = 1,2,3, let xj denote a student's score on the jth exam. Suppose the covariance matrix of the data is 80 84 36 S= 84 117 69 36 69 50 Let y = ₁x1 + ₂x2 + 3x3 be an "index" of student performance with cf + c3 + c3 = 1 and c₁ 2 0. Find the constants C₁,C2,C3 so that the variance of y over the data set is as large as possible. Enter the values of c₁, c2,c3 into the answer box below, separated by commas.
Transcribed Image Text:Suppose three tests are administered to a random sample of college students. Let X₁,...,Xy be observation vectors in R³ that list the three scores of each student, and for j = 1,2,3, let xj denote a student's score on the jth exam. Suppose the covariance matrix of the data is 80 84 36 S= 84 117 69 36 69 50 Let y = ₁x1 + ₂x2 + 3x3 be an "index" of student performance with cf + c3 + c3 = 1 and c₁ 2 0. Find the constants C₁,C2,C3 so that the variance of y over the data set is as large as possible. Enter the values of c₁, c2,c3 into the answer box below, separated by commas.
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