The website has a random decimal generator that will generate a list of random numbers between 0 and 1. What would be the shape of the density curve for the distribution of random numbers generated?

The density curve for a distribution of random numbers generated uniformly between 0 and 1 would be a rectangular shape (also known as a uniform distribution). In this scenario, every value between 0 and 1 has an equal probability of being generated. Specifically, the characteristics of this uniform distribution are: - The minimum value is 0, and the maximum value is 1. - The height of the rectangle is constant and equal to 1 (the total area under the curve must equal 1), which can be calculated as the reciprocal of the range (1 - 0 = 1). - The area under the rectangle, which represents the probability of the random number falling within a certain range, is always equal to the height multiplied by the width of that range. Thus, for any segment of the range from \(a\) to \(b\) (where \(0 \leq a < b \leq 1\)), the probability can be calculated as \(P(a \leq X \leq b) = b - a\). In summary, the shape of the density curve for random decimal numbers uniformly generated between 0 and 1 is a horizontal rectangle from 0 to 1.