Adding random numbers. Generate two random numbers between 0 and 1 and take X to be their sum. The sum X can take any value between 0 and 2. The density curve of X is the triangle shown in Figure 10.7.

0 1 2 Height = 1 FIGURE 10.7 The density curve for the sum of two random numbers, for Exercise 10.15.

This density curve spreads probability between 0 and 2.

(a) Verify by geometry that the area under this curve is 1.

(b) What is the probability that X is less than 1? (Sketch the density curve, shade the area that represents the probability, then find that area. Do this for (c)

also.)

(c) What is the probability that X is less than 0.5?