Exercise 12. Let X, Y, Z ~ N(0,1) be independent. Determine the distribution, expectation and variance of the following random variables: a) X+Y+Z b) x² + y² + Z² Exercise 13. Let X₁,..., X₁~ N(2,02) i.i.d. and Y₁,...,Y₁ ~ N(Hy, ²) i.i.d. with known o². We assume that for each i the random variables X, and Y; are correlated, with Corr(X₁,Y)= 1/2. Define D₂ = X₁ - Y; for all i € {1,...,n}. Finally, let X, Y and D be the averages of the X₁, Y; and D₁, respectively. a) Show that Cov(X₁,Y₁) = 0²/2. b) Determine E(D;) and Var(D;). al Consider the toot for HI... which won the foot atatiatio
Exercise 12. Let X, Y, Z ~ N(0,1) be independent. Determine the distribution, expectation and variance of the following random variables: a) X+Y+Z b) x² + y² + Z² Exercise 13. Let X₁,..., X₁~ N(2,02) i.i.d. and Y₁,...,Y₁ ~ N(Hy, ²) i.i.d. with known o². We assume that for each i the random variables X, and Y; are correlated, with Corr(X₁,Y)= 1/2. Define D₂ = X₁ - Y; for all i € {1,...,n}. Finally, let X, Y and D be the averages of the X₁, Y; and D₁, respectively. a) Show that Cov(X₁,Y₁) = 0²/2. b) Determine E(D;) and Var(D;). al Consider the toot for HI... which won the foot atatiatio
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
Related questions
Question
Exercise 3 pls
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 1 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage