Suppose a circular clothes rack has T; shirts, each of which has a uniformly chosen random color over a set of three possible colors, Red, Blue, or Green (1/3 probability for each color), and assume all the colors are independent. Let X be the number of shirts that share a color with at least one of the two shirts adjacent to it. Find IE[X] and Var(X) (Hint: write X 2 2?:1 Y, for some indicators Y,, and explicitly compute Cov, 3/3).)