Problem 22E
Here are two random variables that are uncorrelated but not independent. Let X and Y have the following joint probability mass function:
a. Use the definition of independence on page 141 to show that X and Y are not independent (in fact \(Y=|X|\), so Y is actually a function of X).
b. Show that X and Y are uncorrelated.
Equation Transcription:
Text Transcription:
p(x,y)
Y=|X|
Step-by-Step Solution:
Answer :
Step 1 of 3:
Given, let X and Y have the joint probability mass function.
x |
y |
p(x,y) |
-1 |
1 |
1/3 |
0 |
0 |
1/3 |
1 |
1 |
1/3 |
Step 2 of 3
Chapter 2.6, Problem 22E is Solved
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Step 3 of 3
