Question: 9.14 Adding random numbers. Generate two random rmmbers between 0 and 1 and take X to be their sum. The sum X can take any

9.14 Adding random numbers. Generate two random rmmbers 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 9.7.

0 1 2 Height 1

(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?

0 1 2 Height 1

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