A random point is picked uniformly inside the triangle on the plane with vertices (0, 0), (0, 2) and (4, 1). Let X be the x-coordinate of this random point. Find the cumulative distribution function F and density function f of X using the following two approaches. Examples 3.19 and 3.9 give guidance. (a) Find F from the connection between probability and area, and then differentiate to find f . (b) Find f with the infinitesimal method illustrated by Example 3.9, and then integrate to find F.