I spent a solid 35 minutes writing out a long and extensive post then the forum software decided I was on the page for too long and erased everything. So here it goes again... This is for studying, it was from a past homework assignment.

I have a joint probability distribution, P(X,Y) that is a 4x4 matrix.

X123411/4 0 1/8 1/8 Y21/8 0 1/16 1/16 31/16 0 1/32 1/32 41/16 0 1/32 1/32

I need to, and cannot, findP(Y|X)andP(X=3|Y).

Below I use the notation P(x,y) to denote the probability at the coordinates (x,y).

My attempt for P(Y|X):

P(Y|X) = Each vector in X..?? (Isn't that just the original table?)

So,

P(Y|X) = { P(Y|X=1), P(Y|X=2), P(Y,X=3), P(Y,X=4) }

(X is across, Y is vertical)

Y / X123411/4 0 1/8 1/8 21/8 0 1/16 1/16 31/16 0 1/32 1/32 41/6 0 1/32 1/32

This is just the original table, but I'm not sure what else P(Y|X) could mean.

My attempt for P(X=3|Y):

I think this wants the probabilities at every point where X=3 and for each Y.

So,

P(X=3|Y) = { P(3,1), P(3,2), P(3,3), P(3,4) }

= { 1/8, 1/16, 1/32, 1/32 }

Any help is appreciated, thanks!