# Binomial and Poisson Distributions Compared

Statistics - investigating the conditions for the discrete Poisson distribution to be used as an approximation to the discrete Binomial distribution. This applet can be used as a calculator for Binomial and Poisson single and cumulative probabilities.

###### Author and programmer: Ron Barrow

TweetInstructions below See also: Binomial and Normal Poisson and Normal Binomial Expansions PRINT

## How to Use this Applet

As you start this program you see a Binomial Distribution - X~B(10,0.5) - displayed as a stick graph. By clicking and dragging the two sliders in the middle of the page `n` can be varied from 2 to 100, and `p` from 0.01 to 0.99.

You can see the values of different Binomial probabilities near the bottom of the screen, and you can change these by sliding the white balls along the baseline of the graph. Try it out for yourself.

Checking the "Poisson" box draws, in yellow, the sticks for the Poisson distribution which has the same mean as the Binomial - Y~Po(5). Notice that the Poisson sticks are drawn just to the left of the Binomial ones so that they can be seen. It also displays some Poisson probabilities to help you compare with the Binomial ones.

Each distribution can be clicked on or off, to help you compare the two distributions. When both distributions are visible, a percentage error is also shown at the bottom to help you further.

Clicking "Reset" returns the screen to the starting position.

Play around with different numbers of trials (`n`) and different probabilities of success (`p`). You should try to judge when one distribution is a good approximation of the other, and when it isn't.

If you check the "Rectangles" box, the Binomial distribution is redrawn with rectangles instead of sticks.

Have fun as you learn by experimenting!