Joint distributions for X, Y, and Z: Y=0 Y=1 Y=0 Y=1 X=0 0.125 0.125 0.405 0.045 X=1 0.125 0.125 0.045 0.405 Z=0 Z=1 a) Find conditional distribution of X and Y given Z=0 b) Find conditional distribution of X and Y given Z=1 c) Show that X and Y are independent given Z d) Find the marginal distribution of X and Y

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Exponential And Logarithmic Functions
Section5.5: Exponential And Logarithmic Models
Problem 4ECP
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Joint distributions for X, Y, and Z:
Y=0
Y=1
Y=0
Y=1
X=0
0.125
0.125
0.405
0.045
X=1
0.125
0.125
0.045
0.405
Z=0
Z=1
a) Find conditional distribution of X and Y given Z=0
b) Find conditional distribution of X and Y given Z=1
c) Show that X and Y are independent given Z
d) Find the marginal distribution of X and Y
e) Show that X and Y are not marginally independent
Transcribed Image Text:Joint distributions for X, Y, and Z: Y=0 Y=1 Y=0 Y=1 X=0 0.125 0.125 0.405 0.045 X=1 0.125 0.125 0.045 0.405 Z=0 Z=1 a) Find conditional distribution of X and Y given Z=0 b) Find conditional distribution of X and Y given Z=1 c) Show that X and Y are independent given Z d) Find the marginal distribution of X and Y e) Show that X and Y are not marginally independent
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