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 in the figure. Height = 1 (a) Which one of the statements verifies by geometry that the area under this curve is 1? The area of a triangle is found from the formula - X base X height. The height equals 1 and the base equals 2. The area of a triangle with a base on the x-axis is the length of the height. In this case the height equals 1. The area of a triangle with a base on the x-axis is half of the length of the base. In our case the base equals 2. O The area of a triangle is found from the formula - x base x height. The height equals 2 and the base equals 1. (b) What is the probability that X is less than 1? You may sketch the density curve, shade the area that represents the probability, and then find that area. (Round your answer to one decimal place.) P(X