Solution Found!
Using the joint pmf from Exercise 4.2-3, find the value of
Chapter 4, Problem 7E(choose chapter or problem)
Using the joint pme from Exercise 4.2-3, find the value of \(E(Y \mid x)\) for \(x=1,2,3,4\). Do the points \([x, E(Y \mid x)]\) lie on the best-fitting line?
Equation Transcription:
Text Transcription:
E(Y|x)
x = 1, 2, 3, 4
[x,E(Y|x)]
Questions & Answers
QUESTION:
Using the joint pme from Exercise 4.2-3, find the value of \(E(Y \mid x)\) for \(x=1,2,3,4\). Do the points \([x, E(Y \mid x)]\) lie on the best-fitting line?
Equation Transcription:
Text Transcription:
E(Y|x)
x = 1, 2, 3, 4
[x,E(Y|x)]
ANSWER:
Step 1 of 12:
Lex the joint probability mass function of X and Y be
f(x,y)=; (x,y)=(0,1),(1,0),(2,1)
The number of variables corresponding to x is not equal to the number of variables corresponding to y. So the support is not rectangular. Hence X and Y are dependent.
Mean of X,=1 and mean of Y,
=
.
Therefore
Cov(X,Y)=E(XY)-
=(0)(1)+(1)(0)
+(2)(1)
-1(
)
=0+0+-
=0
Thus correlation coefficient becomes equal to 0, which implies X and Y are independent. But we have that X and Y are dependent.