Generate two random numbers between 0 and 1 and take to be their sum. Then Y is

Question

Generate two random numbers between 0 and 1 and take to be their sum. Then Y is a continuous random variable that can take any value between 0 and 2. The density curve of Yis the triangle shown in the figure below Height = 1 (a) What is the area under the curve? (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. Enter your answer to one decimal (c) what is the probability that is less than 1.5? (Sketch the density curve, shade the area that represents the probability, then find that area. Round your answer to three decimal places.) 719

Explanation / Answer

We need to subtract the total are which is 1 and the area of smaller triangle from 1. Smaller triange has base of 0.5 i.e 2-1.5 =0.5 and therefore the height is also 0.5 (because the height is 1 and distance between height and 2 is also 1 and thus angle is 45 degrees), area of smaller triangle is (0.5*0.5)/2 =0.125

thus answer is 1-0.125=0.975

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