Example 3.12. Let X, Y and Z be jointly continuous random variables with joint PDF is given by: fx.y.z(x, y, z) = (12r°yz)I0,1)(z)I(0,1)(y)I0,1)(2) Recall that fx(x) =(3r²)I(0,1)(z) fy(y) =(2y)I(0.1)(») fz(2) =(2=)I(0,1)(2) Are X,Y and Z independent? To show that X, Y and Z are independent, you need to show that fx,y(r, y) =fx(r) × fy(y) fx,z(x, z) =fx(r) × fz(z) fy,z(y, 2) =fy(y) × fz(2) fx.y.z(x, y, z) =fx(1) × fy(y) × fz(z)
Example 3.12. Let X, Y and Z be jointly continuous random variables with joint PDF is given by: fx.y.z(x, y, z) = (12r°yz)I0,1)(z)I(0,1)(y)I0,1)(2) Recall that fx(x) =(3r²)I(0,1)(z) fy(y) =(2y)I(0.1)(») fz(2) =(2=)I(0,1)(2) Are X,Y and Z independent? To show that X, Y and Z are independent, you need to show that fx,y(r, y) =fx(r) × fy(y) fx,z(x, z) =fx(r) × fz(z) fy,z(y, 2) =fy(y) × fz(2) fx.y.z(x, y, z) =fx(1) × fy(y) × fz(z)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 44E
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Transcribed Image Text:Example 3.12. Let X, Y and Z be jointly continuous random variables with joint PDF is given
by:
fx.x.z(x, y, 2) = (12x²yz)[(0,1)(x)/(0,1)(y)!0.1)(2)
Recall that
fx(x) =(3x²)[0,1)(x)
fy(y) =(2y)I(0,1)(y)
fz(2) =(22)I(0,1)(2)
Are X,Y and Z independent?
To show that X, Y and Z are independent, you need to show that
fx.y(r, y) =fx(x) ×x fy(y)
fx,z(x, z) =fx(x) × fz(2)
fy.z(y, z) =fy(y) × fz(2)
fx,x.z(x, y, z) =fx(r) × fy(y) × fz(z)
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