Q 6.1. Suppose Z = (Z₁, Z2, Z3) is a standard multi-variate Gaussian random variable i.e., fori ≤ 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 onerandom variables, (1)-(4), on the right. Pair up according to "equal in distribution" and explainbriefly your reasoning.(a)X₁X2=(√2)X₁(b) (x₂)-(2₂2₂)=Z₁X₁ 3/√√2√2X₂=IV2) (21)01/√√21/√2 (Z₁(c)31(¹) (X) - (11) (2)(d1(1) (2)-()) (²)=Y₂(2) (Y/₁2)(12) = (1/✓/²2²(3)1/2) (²)1/√√2 1/√√21/√√2 -1/√2,2 2 √2(X) - (² : ¹3) (2)10(4) (1/12)(12) - (² 1) (²2)=

Given that be a standard multi-variate Gaussian random variable.For are i.i.d. random variables.

Answered: Q 6.1. Suppose Z = (Z1, Z2, Z3) is a…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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