Binomial Distribution
The binomial distribution is an important discrete distribution. It gives the probability of the number of "successes," in a sequence of n independent binary trials.
Resources
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Virtual Galton board:
Bean Machine
This applet allows users to drag sliders to change the number of bins (n) on a Galton board with probability of success p = 0.5. The applet animates the creation of a binomial distribution. This applet can also be used to demonstrate the normal approximation to the binomial distribution, since users can see that the distribution begins to look like a normal curve as we increase the number of bins (n).
Author: © 2022 Milan Valasek, University of Sussex.
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Visualizing the binomial distribution:
Binomial Distribution Visualization
This applet allows users to drag sliders to change the probability of success (p) and enter the number of trials (n) in the blank box. After setting these two values, the applet displays the resulting binomial distribution of the number of successes. The applet can also display probabilities, obtained by clicking the buttons "Find probabilities for regions using Cut Points" and "Create a table of all binomial probabilities."
Author: Bruce Dudek at the University at Albany.
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Calculating probabilities on a binomial distribution:
Binomial Distribution Calculator
This web calculator allows users to specify the number of trials (n) and probability of success (p). After finishing the steps, the calculator will show a plot of the probability mass function (pmf). The calculator can also compute the probability of a value x. The user can access instructions by clicking the "Help" button.
Author: © 2021 Matt Bognar, Department of Statistics and Actuarial Science, University of Iowa.