Question: 12.16 Adding Random Numbers. Generate two random numbers between 0 and 1 and take X to be their sum. The sum X can take any

12.16 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 12.7.

(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 fi nd that area. Do this for part

(c) also.)

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

0 1 2 Height 1

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