A random vector T = (X, Y)Ã has the probability density function 0 ≤ x ≤ 1 and - x ≤ y ≤ x fr(x, y) = { k (1 + x) 0 otherwise where k > 0.
(a) Sketch the region on which fr(x,y) is positive.
(b) Using a double integral with vertical strips, calculate the value of k which makes fò a probability density function (p.d.f.).
(c) Explain why you would need to use two separate double integrals to calcu- late k if you were using horizontal strips.