Question 4.106

4.106 The sum of two uniform random numbers.

Generate two random numbers between 0 and 1 and take to be their sum. Then is a continuous random variable that can take any value between 0 and 2. The density curve of is the triangle shown in Figure 4.15.

  1. Verify by geometry that the area under this curve is 1.
  2. What is the probability that is less than 1? (Sketch the density curve, shade the area that represents the probability, then find that area. Do this for part (c) also.)
  3. What is the probability that is greater than 0.6?