Interactive element. Hover over the figure above to adjust the value at which we evaluate the cdf. Observe how the values change in both subplots. Do you see a pattern behind high probability density regions in the subplot on the left, and the corresponding steepness in the subplot to the right?
Cumulative Density Functions
Cumulative Density Functions
The cumulative density function (cdf) is obtained by integrating a probability density function (pdf) from -∞ to the value x at which the cdf is being evaluated. In consequence, the output of a cdf represents the probability of x taking on a value smaller or equal than the value at which the cdf is being evaluated. Since every pdf must integrate up to 1, the maximum value of a cdf is also 1.