Page 142, 2.6.2.* Let f(x1,x2,X3)=exp[-(x1 + x2 + x3)], 0 < x₁ <∞, 0 < x₂ < ∞, 0 < x3 <∞, = zero elsewhere, be the joint pdf of X₁, X2, X3. (a) Compute P (X₁ < 3X₂) and P (X₁ = 3X₂). (b) Determine the mgf of X₁+2X2+2X3. Are X₁, X₂, and X3 random variables independent and identically distributed? Give reasoning.

Page 142, 2.6.2.* Let f(x1,x2,X3)=exp[-(x1 + x2 + x3)], 0 < x₁ <∞, 0 < x₂ < ∞, 0 < x3 <∞, = zero elsewhere, be the joint pdf of X₁, X2, X3. (a) Compute P (X₁ < 3X₂) and P (X₁ = 3X₂). (b) Determine the mgf of X₁+2X2+2X3. Are X₁, X₂, and X3 random variables independent and identically distributed? Give reasoning.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 17EQ

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