An arbitrary point (X, Y ) is drawn from the square [−1, 1] × [−1, 1]. This means that for any region G in the plane, the probability that (X, Y ) is in G, is given by the area of G∩ divided by the...

An arbitrary point (X, Y ) is drawn from the square [−1, 1] × [−1, 1]. This means that for any region G in the plane, the probability that (X, Y ) is in G, is given by the area of G∩ divided by the area of , where denotes the square [−1, 1] × [−1, 1]: P(

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

b. Check that X and Y are two independent, U(−1, 1) distributed random variable