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joint pdf of the random variables X₁ and X2, show that X₁ and X₂ are independent and that M(t1, t₂) = (1-t₁)-¹(1-t₂)-¹, t₂ <1, t₁ < 1. Also show that E(et(x₁+x₂)) = (1-1)-², t<1. Accordingly, find the mean and the variance of Y = X₁ + X₂.

joint pdf of the random variables X₁ and X2, show that X₁ and X₂ are independent and that M(t1, t₂) = (1-t₁)-¹(1-t₂)-¹, t₂ <1, t₁ < 1. Also show that E(et(x₁+x₂)) = (1-1)-², t<1. Accordingly, find the mean and the variance of Y = X₁ + X₂.

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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2.5.6. If f(x1, x₂) = е-1-2, 0 < x < ∞, 0 < x₂ <∞, zero elsewhere, is the joint pdf of the random variables X₁ and X₂, show that X₁ and X₂ are independent and that M (t1, 12) = (1-t₁)-¹(1-t₂)-¹, t₂ <1, t₁ < 1. Also show that E(e¹(x₁+x₂)) = (1-t)-², t<1. Accordingly, find the mean and the variance of Y = X₁ + X₂.
Transcribed Image Text:2.5.6. If f(x1, x₂) = е-1-2, 0 < x < ∞, 0 < x₂ <∞, zero elsewhere, is the joint pdf of the random variables X₁ and X₂, show that X₁ and X₂ are independent and that M (t1, 12) = (1-t₁)-¹(1-t₂)-¹, t₂ <1, t₁ < 1. Also show that E(e¹(x₁+x₂)) = (1-t)-², t<1. Accordingly, find the mean and the variance of Y = X₁ + X₂.
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