A continuous random variable (RV) X has support X = [l, u], for given l, u (with l < u), and a probability density function (PDF) that is linearly increasing over the support, i.e., fX (x) = mx + b, for m, b to be determined. The PDF evaluated at x = l is fX (l) = 0. Please do the following:

Give expressions for the PDF fX (x) in terms of l, u, i.e., find expressions for m, b in terms of l,u. Make sure you give an answer for all possible values of x, i.e., x < l, x [l,u], and x > u. Hint: use the facts that fX (l) = 0 and that the density must integrate to one.