image 4.60 The sum of two uniform random numbers. Generate two random numbers between 0 and 1 and take Y to be their sum. Then Y is a continuous random variable that can take any value between 0 and 2. The density curve of Y is the triangle shown in Figure 4.12.

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

  2. (b) What is the probability that Y 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. (c) What is the probability that Y is greater than 1.5?

  4. (d) What is the probability that Y is greater than 0.5?

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Figure 4.12 The density curve for the sum Y of two random numbers, Exercise 4.60.