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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)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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)
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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