Suppose (0) (ii) (iii) X, has a pdf f(x₁) = x₁²e-x²³/ 16 0 X₂ has a pdf f₂(x₂)=< $₂² 4 0 X, and X, are independent. Examine whether Y₁ = X₁ + X, and Y₂ ; 0

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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Suppose
(i)
(ii)
(iii)
X, has a pdf f(x₁) =<
x₁²e-²/2
16
0
X₂ has a pdf f₂ (x₂) = {
x₂²e-x₂²³/2
4
0
X, and X₂ are independent.
Examine whether Y₁ = X₁ + X, and
Y₂
=
; 0<x₁ <∞⁰
; otherwise,
X₁
X₁ + X₂
; 0< x₂ <∞0
; otherwise,
are independent.
Transcribed Image Text:Suppose (i) (ii) (iii) X, has a pdf f(x₁) =< x₁²e-²/2 16 0 X₂ has a pdf f₂ (x₂) = { x₂²e-x₂²³/2 4 0 X, and X₂ are independent. Examine whether Y₁ = X₁ + X, and Y₂ = ; 0<x₁ <∞⁰ ; otherwise, X₁ X₁ + X₂ ; 0< x₂ <∞0 ; otherwise, are independent.
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