(i) (ii) (iii) X, has a pdf f(x₁) = { X₂ has a pdf f₂(x₂) =< x₂ 16 0 x₂²e-x₂²/2 4 0 X, and X₂ are independent. Examine whether Y₁ = X₁ + X₂ and Y₂ ; 0

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Question
(i)
(ii)
(iii)
X, has a pdf f(x₁) =
x₁²e-x²³/2
16
0
X₂ has a pdf f₂(x₂2₂) = ²
x₂²e²1₂²³/2
4
0
X, and X₂ are independent.
Examine whether Y₁ = X₁ + X₂ and Y₂
=
; 0<x₁ <∞0
; otherwise,
X₁
X₁ + X₂
; 0<x₂ <∞0
; otherwise,
are independent.
Transcribed Image Text:(i) (ii) (iii) X, has a pdf f(x₁) = x₁²e-x²³/2 16 0 X₂ has a pdf f₂(x₂2₂) = ² x₂²e²1₂²³/2 4 0 X, and X₂ are independent. Examine whether Y₁ = X₁ + X₂ and Y₂ = ; 0<x₁ <∞0 ; otherwise, X₁ X₁ + X₂ ; 0<x₂ <∞0 ; otherwise, are independent.
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