3. Let Y₁, Y2, Y3, Y₁ ~ N(B0, 0²), where Y's are independent. Given the vector Y = [Y₁, Y2, Y3, Y4] and orthonormal coordinate system U₁ = [1,1, 1, 1]T, U₂ = †[−1, −1, 1, 1]T, U3 = [1,1,0,0]ª and U₁ = [0, 0, −1, 1]T. Answer the following questions. You have to show all your work. i) Find the constants C₁, C₂, C3, C4 for which Y = C₁U₁ + C₂U2₂ + C3U3 + C₁U₁. Provide ex- pressions of C₁, C2, C3, C4 explicitly. ii) What is the distribution of c₁? Provide its name and parameters explicitly. Justify your answer. iii) What is the distribution of c²/0². Provide its name and parameters explicitly. Justify your answer.
3. Let Y₁, Y2, Y3, Y₁ ~ N(B0, 0²), where Y's are independent. Given the vector Y = [Y₁, Y2, Y3, Y4] and orthonormal coordinate system U₁ = [1,1, 1, 1]T, U₂ = †[−1, −1, 1, 1]T, U3 = [1,1,0,0]ª and U₁ = [0, 0, −1, 1]T. Answer the following questions. You have to show all your work. i) Find the constants C₁, C₂, C3, C4 for which Y = C₁U₁ + C₂U2₂ + C3U3 + C₁U₁. Provide ex- pressions of C₁, C2, C3, C4 explicitly. ii) What is the distribution of c₁? Provide its name and parameters explicitly. Justify your answer. iii) What is the distribution of c²/0². Provide its name and parameters explicitly. Justify your answer.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
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[Regression Analysis] How do you solve this?
![3. Let Y₁, Y2, Y3, Y4 ~ N(30, 02), where Y's are independent.
Given the vector Y = [Y₁, Y2, Y3, Y4] and orthonormal coordinate system U₁ = [1,1, 1, 1]T,
U₂ = [1, −1, 1, 1]T, U3 = [1,1,0,0] and U₁ = [0,0,−1, 1]T.
Answer the following questions. You have to show all your work.
i) Find the constants C₁, C2, C3, C4 for which Y C₁U₁ + C₂U₂ + C3U3 + C₁U₁. Provide ex-
pressions of C₁, C2, C3, C4 explicitly.
ii) What is the distribution of c₁? Provide its name and parameters explicitly. Justify
your answer.
iii) What is the distribution of c/o². Provide its name and parameters explicitly. Justify
your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4113e1c-31b1-4c6c-bcf1-9ebcadc67f7b%2F3270e0f1-c658-4daf-a5fc-3f4fc8eb8f20%2Fto0sv7h_processed.png&w=3840&q=75)
Transcribed Image Text:3. Let Y₁, Y2, Y3, Y4 ~ N(30, 02), where Y's are independent.
Given the vector Y = [Y₁, Y2, Y3, Y4] and orthonormal coordinate system U₁ = [1,1, 1, 1]T,
U₂ = [1, −1, 1, 1]T, U3 = [1,1,0,0] and U₁ = [0,0,−1, 1]T.
Answer the following questions. You have to show all your work.
i) Find the constants C₁, C2, C3, C4 for which Y C₁U₁ + C₂U₂ + C3U3 + C₁U₁. Provide ex-
pressions of C₁, C2, C3, C4 explicitly.
ii) What is the distribution of c₁? Provide its name and parameters explicitly. Justify
your answer.
iii) What is the distribution of c/o². Provide its name and parameters explicitly. Justify
your answer.
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