Suppose a basketball player has an 80 percent chance of making a free throw. He has been fouled, and has two free throws. If a free throw is made, its counts as one point. Let $X$ and $Y$ be the number of points from the first and second free throw respectively. Figure out the joint probabilities for $X$ and $Y$, the expected number of points from the two free throws, and the variance for this number of points, when:
a) each free throw is an independent event
b) $P(Y=1\mid X=1)=0.9$ and $P(Y=1\mid X=0)=0.4$ so that making the first free throw raises the probability of making the second free throw.
So I've pretty much done part a but the only thing I'm confused about is when I find the expected number of points from the two free throws its less than 1. Should it be that way? Than, for part b it only gives me two of the probabilities and I'm a little confused about how to find the other two. I tried setting it up into a two by two box with X values on top and Y values on the side but still couldn't figure that out. Any input would be appreciated. Thanks!