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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please show step-by-step solution and do not skip steps. Explain your entire process in great detail.
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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 7 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
