Question 8.80
49. Generate two random real numbers between 0 and 1 and take their sum. The sum can take any value between 0 and 2. The density curve is the shaded triangle shown in Figure 8.29.
Figure 8.29: Figure 8.29 The density curve for the sum of two random numbers, for Exercise 49.
- Verify by geometry that the area under this curve is 1.
- What is the probability that the sum is less than 1? Sketch the density curve, shade the area that represents the probability, and then find that area.
- What is the probability that the sum is less than 0.5? Sketch the density curve, shade the area that represents the probability, and then find that area.
49.
(a)
(b) The probability is 1/2 by symmetry or finding the area:
(c) The area representing this event is
A-23