Plots of the Chi-square distribution

This page collects some plots of the Chi-square distribution. The plots help us to understand how the shape of the Chi-square distribution changes when the degrees of freedom parameter is changed.

Density plots

The following plot contains the graphs of two Chi-square probability density functions. The first graph (blue line) is the probability density function of a Chi-square random variable with degrees of freedom. The second graph (red line) is the probability density function of a Chi-square random variable with degrees of freedom. Increasing the number of degrees of freedom increases the probability density of larger values. The thin vertical lines indicate the means of the two distributions.

The following plot also contains the graphs of two Chi-square probability density functions. The first graph (blue line) is the probability density function of a Chi-square random variable with degrees of freedom. The second graph (red line) is the probability density function of a Chi-square random variable with degrees of freedom. Increasing the number of degrees of freedom increases the probability density of larger values. The thin vertical lines indicate the means of the two distributions.