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© ↑ ↓ ± ▼ 1.3. Question 2 Let X and Є be independent normally distributed random variables such that ✗~ N(5, 4) and € ~ N(0, 9). Let Y be a random variable given by Y=1+2X+ €. Compute: (a) (b) (a) E(Y) (b) Var(Y) (c) Cov(X, Y) (d) Corr(X, Y) (e) What is the value of the ratio Cov(X,Y)/Var(X) ? (f) If Y = 1 + 3X + € instead, what would be the value of Cov(X, Y)/Var(X) ? (g) If Y = 1 + 7X + € instead, what would be the value of Cov(X, Y)/Var(X)? (c) (d) (e) (f) (g)

© ↑ ↓ ± ▼ 1.3. Question 2 Let X and Є be independent normally distributed random variables such that ✗~ N(5, 4) and € ~ N(0, 9). Let Y be a random variable given by Y=1+2X+ €. Compute: (a) (b) (a) E(Y) (b) Var(Y) (c) Cov(X, Y) (d) Corr(X, Y) (e) What is the value of the ratio Cov(X,Y)/Var(X) ? (f) If Y = 1 + 3X + € instead, what would be the value of Cov(X, Y)/Var(X) ? (g) If Y = 1 + 7X + € instead, what would be the value of Cov(X, Y)/Var(X)? (c) (d) (e) (f) (g)

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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© ↑ ↓ ± ▼ 1.3. Question 2 Let X and Є be independent normally distributed random variables such that ✗~ N(5, 4) and € ~ N(0, 9). Let Y be a random variable given by Y=1+2X+ €. Compute: (a) (b) (a) E(Y) (b) Var(Y) (c) Cov(X, Y) (d) Corr(X, Y) (e) What is the value of the ratio Cov(X,Y)/Var(X) ? (f) If Y = 1 + 3X + € instead, what would be the value of Cov(X, Y)/Var(X) ? (g) If Y = 1 + 7X + € instead, what would be the value of Cov(X, Y)/Var(X)? (c) (d) (e) (f) (g)
Transcribed Image Text:© ↑ ↓ ± ▼ 1.3. Question 2 Let X and Є be independent normally distributed random variables such that ✗~ N(5, 4) and € ~ N(0, 9). Let Y be a random variable given by Y=1+2X+ €. Compute: (a) (b) (a) E(Y) (b) Var(Y) (c) Cov(X, Y) (d) Corr(X, Y) (e) What is the value of the ratio Cov(X,Y)/Var(X) ? (f) If Y = 1 + 3X + € instead, what would be the value of Cov(X, Y)/Var(X) ? (g) If Y = 1 + 7X + € instead, what would be the value of Cov(X, Y)/Var(X)? (c) (d) (e) (f) (g)
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