Hi, I got kind of stuck on this problem. I believe I have part (a) and (e) correct but if possible ensuring it is correct would be great. The rest I am not too sure on how to do, my professor has not done a great job of showing us expected value and variance and I am having trouble with it. All help is greatly appreciated, thanks!!

4. The grid shown below has 9 points and 12 edges connecting them. The distance between two points is the smallest number of edges needed to connect them. For example, a single vertical edge connects points 1 and 4, hence the distance between them is 1, similarly, points 8 and 6 are distance 2 apart, the distance between points 7 and 3 is 4, etc. Two points with distance one, for example, points 5 and 6, are called adjacent. Choose two distinct random points in the grid, namely every pair is equally likely, and nd: (a) The probability that the two points are adjacent. (b) The expected distance between the two points. (c) The variance of the distance between them. ((1) The expected distance between them if we know that they are not adjacent. (e) The probability that the distance between the points is Z 2 if it is 5 3. (f) The probability that one of the points is at the center of the grid (point 5) if the distance between the two points is l