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blem #5: 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 Problem #5: 10 20 23 80 44 53 S = 20 23 44 Let y = C₁x₁ + ₂x2 + Cc3x3 be an "index" of student performance with c² + c3 + c3 = 1 and c₁0. 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. numbers correct to 2 decimals

blem #5: 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 Problem #5: 10 20 23 80 44 53 S = 20 23 44 Let y = C₁x₁ + ₂x2 + Cc3x3 be an "index" of student performance with c² + c3 + c3 = 1 and c₁0. 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. numbers correct to 2 decimals

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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Problem #5: 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 x; denote a student's score on the th exam. Suppose the covariance matrix of the data is Problem #5: S = 10 20 23 20 80 44 23 44 53 Let y = 01x1 + 02x2 + c3x3 be an "index" of student performance with c + 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 commas. numbers correct to 2 decimals
Transcribed Image Text:Problem #5: 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 x; denote a student's score on the th exam. Suppose the covariance matrix of the data is Problem #5: S = 10 20 23 20 80 44 23 44 53 Let y = 01x1 + 02x2 + c3x3 be an "index" of student performance with c + 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 commas. numbers correct to 2 decimals
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