Let X and Y be as in the triangle example in Exercise 9.15. Recall from Exercise 9.16 that X and Y represent the minimum and maximum coordinate of a point that is drawn from the unit square: X =...

Let X and Y be as in the triangle example in Exercise 9.15. Recall from Exercise 9.16 that X and Y represent the minimum and maximum coordinate of a point that is drawn from the unit square: X = min{U, V } and Y = max{U, V }

a. Show that E[X]=1/3, Var(X)=1/18, E[Y ]=2/3, and Var(Y )=1/18. Hint: you might consult Exercise 8.15.

b. Check that Var(X + Y )=1/6, by using that U and V are independent and that X + Y = U + V .

c. Determine the covariance Cov(X, Y ) using the results from a and b.