Suppose that the joint probability density function of (X, Y) is given by
(a) Prove or disprove: X and Yare independent if and only if X and Yare uncorrelated.
An isosceles triangle is formed as indicated in the sketch.
(b) If (X. Y) has the joint density given above, pick IX to maximize the expected area of the triangle.
(c) What is the probability that the triangle falls within the unit square with corners at (0, 0), (1, 0), (1, 1), and (0, 1)?
(d) Find the expected length of the perimeter of the triangle.