Plots of the uniform distribution

This page collects some plots of the uniform distribution. The plots help us to understand how the shape of the uniform distribution changes when the lower bound and the upper bound of its support are changed.

Density plots

The following plot contains the graphs of two uniform probability density functions. The first graph (blue line) is the probability density function of a uniform random variable with support . The second graph (red line) is the probability density function of a uniform random variable with support . The two random variables have different supports, but their two supports have the same length. Therefore, since the uniform density is constant and inversely proportional to the length of the support, the two random variables have the same constant density over their respective supports.

The following plot contains the graphs of two uniform probability density functions. The first graph (blue line) is the probability density function of a uniform random variable with support . The second graph (red line) is the probability density function of a uniform random variable with support . The two random variables have different supports, and the length of is twice the length of . Therefore, since the uniform density is constant and inversely proportional to the length of the support, the second random variable has a constant density which is half the constant density of the first one.