Probability Distributions

This mathlet shows the probability density function (pdf) and cumulative distribution function (cdf) for several discrete and continuous probability distributions. The mathlet also displays the total probability between two limits.

Both pdf and cdf graphs show the same information in a color coordinated way, e.g. in both graphs the limits for probability \(l\) and \(u\) are shown in blue and green respectively and the total probability between \(l\) and \(u\) is shown in orange.

Graphs

The upper graph shows the probability density function or probability mass function for the selected distribution. The probability between the \(x\) values of the vertical blue and green lines is highlighted in orange and the total probability in this region is shown at the lower right of the mathlet.
The lower graph shows the cumulative probability distribution for the selected distribution. The probability between the \(x\) values of the vertical blue and green lines is shown as an orange line towards the left side of the graph.

Controls

The Distributions radio buttons are used to choose the probability distribution to display. Selecting a distribution reveals sliders to control the parameters of that distribution.
The \(\boldsymbol{x}\)-min, \(\boldsymbol{x}\)-max slider sets the horizontal graphing limits in both pdf and cdf graphs.
When Stem display is selected the discrete probability functions are shown using a stem plot. When it is not selected they are done using a box plot. This control is only visible when a discrete distribution is selected.
The probability limit lines are the vertical lines in both graphs showing the limits for the computed probability. They can be dragged with the mouse to change the limits. The blue line controls the lower limit \(l\) and the green line controls the upper limit \(u\). The probability between the two limits is shown in orange. The values of \(l, u\) and the probability are shown near the bottom right of the mathlet.
The \(\boldsymbol{x}\) and \(\boldsymbol{y}\) readouts show the position of the mouse when it is in either graphing window. They are placed just above the readouts for \(l\) and \(u\).