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!