Let the pair (X, Y ) be drawn arbitrarily from the triangle ∆ with vertices (0, 0), (0, 1), and (1, 1). a. Use Figure 9.5 to show that the joint distribution function F of the pair (X, Y ) satisfies...

Let the pair (X, Y ) be drawn arbitrarily from the triangle ∆ with vertices (0, 0), (0, 1), and (1, 1).

a. Use Figure 9.5 to show that the joint distribution function F of the pair (X, Y ) satisfies

b. Determine the joint probability density function f of the pair (X, Y ).

c. Show that
X(x)=2 − 2x for x between 0 and 1 and that fY (y)=2y for y between 0 and 1.