The sum of two uniform (0, 1) random variables. Let X represent the sum of these two uniformly distributed (0,1) random variables, as shown in Figure 5.8. Recall that the area of a triangle = ½hb. Use Figure 5.8 to determine:

(a) Pr(X < 1).

(b) Pr(X > 1.5).

(c) Pr(1 < X < 1.5).