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.X₁(a)X₂(b) (x₂) - (2)(c) (x²) - (¹/1² 1/√²) (2₁)(3/√2=√2=(V2)Z₁(d) (x) - (1) (²)X2Y₁(9)-(-) (2)(1=1)Y₂(1)Y₁(²) (4) - (1/²(3)(1/√√21/√2-1/√2)(x₁) = (²₁ ² ✓/³²) (3)2 2 √21Z3Y₁→ ()-())(4)=Y₂1/2) (2)1)(2)

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)

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Chapter1: Combinatorial Analysis

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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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