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6.1. Suppose 2 = (21, 22, 23) is a standard multi-variate Gaussian random variable i.e., for i≤ 3, Zi~ N(0, 1) are i.i.d. random variables. Each of the random variables, (a)-(d), on the left is equal in distribution to exactly one random variables, (1)-(4), on the right. Pair up according to "equal in distribution" and explain briefly your reasoning. X₁ X₂) (a) (b) (x₂) = (²₂) X2 (d) = (V2) Z₁ (c) (X₂) = (3/1/² ¹/√²) (2/1₂) X2 0 (X) = (1²1) (²) - ()-(-) (²) (1) (²) (11) - (1/² 1/7/2) (2) (1/√2 1/√2 Y2 2 2 √2 (3) (X) = (² ² √2) (4) (2) - (1) (²) Z₁ Z₂ Z3

6.1. Suppose 2 = (21, 22, 23) is a standard multi-variate Gaussian random variable i.e., for i≤ 3, Zi~ N(0, 1) are i.i.d. random variables. Each of the random variables, (a)-(d), on the left is equal in distribution to exactly one random variables, (1)-(4), on the right. Pair up according to "equal in distribution" and explain briefly your reasoning. X₁ X₂) (a) (b) (x₂) = (²₂) X2 (d) = (V2) Z₁ (c) (X₂) = (3/1/² ¹/√²) (2/1₂) X2 0 (X) = (1²1) (²) - ()-(-) (²) (1) (²) (11) - (1/² 1/7/2) (2) (1/√2 1/√2 Y2 2 2 √2 (3) (X) = (² ² √2) (4) (2) - (1) (²) Z₁ Z₂ Z3

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Q 6.1. Suppose Z = (Z1, Z2, Z3) is a standard multi-variate Gaussian random variable i.e., for i ≤ 3, Zi~ N(0, 1) are i.i.d. random variables. Each of the random variables, (a)-(d), on the left is equal in distribution to exactly one random variables, (1)-(4), on the right. Pair up according to "equal in distribution" and explain briefly your reasoning. (a) (X₂) (¹) (X) = (2) 1/√2 (Ⓒ) (x₂) - (3/1² ¹1/1²) (2) (c = 2 0 = 2 Z₁ 1) (²) 3 (4¹) (X) = (²¹) (1) (2) (3) Y₁ 1 (29) - ()) (2) = Y₂ 1 Y₁ (121) = (1/² √₂) (2) (1/√2 1/√2 /2 −1/√√2, Y₂ X₁ X₂ = 22 1 1 2 0 Y₁ 2 1 (4) (2)) = (²) (²) 1 1 Z₁ Z₂ Z3
Transcribed Image Text:Q 6.1. Suppose Z = (Z1, Z2, Z3) is a standard multi-variate Gaussian random variable i.e., for i ≤ 3, Zi~ N(0, 1) are i.i.d. random variables. Each of the random variables, (a)-(d), on the left is equal in distribution to exactly one random variables, (1)-(4), on the right. Pair up according to "equal in distribution" and explain briefly your reasoning. (a) (X₂) (¹) (X) = (2) 1/√2 (Ⓒ) (x₂) - (3/1² ¹1/1²) (2) (c = 2 0 = 2 Z₁ 1) (²) 3 (4¹) (X) = (²¹) (1) (2) (3) Y₁ 1 (29) - ()) (2) = Y₂ 1 Y₁ (121) = (1/² √₂) (2) (1/√2 1/√2 /2 −1/√√2, Y₂ X₁ X₂ = 22 1 1 2 0 Y₁ 2 1 (4) (2)) = (²) (²) 1 1 Z₁ Z₂ Z3
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