# Correlation Coefficient dealing with discretely distributed variables

I'm a bit stuck on this practice problem I have for my HS business stats class. I'd appreciate any help to get the solutions. Thank you.

Exercise #22: Let X and Y be discretely distributed random variables such that Pr[X =1,Y =1]=Pr[X =2,Y =−2]=Pr[X =3,Y =1]=1/3.

(a) Find the correlation coefficient between X and Y .

(b) Define a function f by f(x) = 1 if x=1 or x=3, f(x) = -2 otherwise.

Then E[Y |X] = f(X).

(...For this part of the exercise I was thinking that I have to calculate the mean square error in predicting Y using the function f(x), and maybe it also has something to do with conditional expectation.)

(c)Are X and Y independent? (I was thinking that they are independent)

Again, thank you to anyone who's willing to help a girl out!

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a) can be solved by straightforward plugging and chugging into known formulas -- they may even be given in your textbook --. Where are you having difficulties in this? –  Dilip Sarwate Jan 24 '13 at 4:22
I had a little difficulty because I could not find the known formulas at the time, but I just did so I got part A now... –  Jenna K. Jan 24 '13 at 5:00
b) can be solved by straightforward plugging and chugging into known formulas -- they may even be given in your textbook --. Where are you having difficulties in this? –  Did Jan 24 '13 at 6:57