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# Let the joint pmf of X and Y be (a) Are X and Y ISBN: 9780321923271 41

## Solution for problem 7E Chapter 4.2

Probability and Statistical Inference | 9th Edition

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Problem 7E

PROBLEM 7E

Let the joint pmf of X and Y be (a) Are X and Y independent?

(b) Calculate Cov(X,Y) and ρ.

This exercise also illustrates the fact that dependent random variables can have a correlation coefficient of zero.

Step-by-Step Solution:

Step 1 of  4

The given pmf is (x,y) S={(0,0), (1,1), (1,-1), (2,0)}

Arrange the given values into tabular form 0 1 2 -1 0 1/4 0 1/4 0 1/4 0 1/4 2/4 1 0 1/4 0 1/4 1/4 2/4 1/4 1

Step 2 of  4

a) If X and Y are independent then it satisfies E(XY)=E(X)E(Y)

E(X)=  = 0(1/4)+1(2/4)+2(1/4)

= 4/4

=1

E(Y)=  = -1(1/4)+0(2/4)+1(1/4)

= 1/4-1/4

=0

Step 3 of 4

Step 4 of 4

##### ISBN: 9780321923271

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