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 given Figure.
(a) Verify by geometry that the area under this curve is 1.
(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 (c) also.
(c) What is the probability that Y is greater than 0.6?