To plot the probability mass function for a binomial distribution in R, we can use the following functions:
- dbinom(x, size, prob) to create the probability mass function
- plot(x, y, type = ‘h’) to plot the probability mass function, specifying the plot to be a histogram (type=’h’)
To plot the probability mass function, we simply need to specify size (e.g. number of trials) and prob (e.g. probability of success on a given trial) in the dbinom() function.
For example, the following code illustrates how to plot a probability mass function for a binomial distribution with size = 20 and prob = 0.3:
success
The x-axis shows the number of successes and the y-axis shows the probability of obtaining that number of successes in 20 trials.
We can add a title, change the axes labels, and increase the line width to make the plot more aesthetically pleasing:
success
You can use the following code to obtain the actual probabilities for each number of successes shown in the plot:
#prevent R from displaying numbers in scientific notation options(scipen=999) #define range of successes success #display probability of success for each number of trials dbinom(success, size=20, prob=.3) [1] 0.00079792266297612 0.00683933711122388 0.02784587252426865 [4] 0.07160367220526231 0.13042097437387065 0.17886305056987975 [7] 0.19163898275344257 0.16426198521723651 0.11439673970486122 [10] 0.06536956554563482 0.03081708090008504 0.01200665489613703 [13] 0.00385928193090119 0.00101783259716075 0.00021810698510587 [16] 0.00003738976887529 0.00000500755833151 0.00000050496386536 [19] 0.00000003606884753 0.00000000162716605 0.00000000003486784
Additional Resources
An Introduction to the Binomial Distribution
Understanding the Shape of a Binomial Distribution