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)]

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.