To plot the probability mass function for a Poisson distribution in R, we can use the following functions:

**dpois(x, lambda)**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 **lambda**** **(e.g. the rate of occurrence of events) in the **dpois() **function.

For example, the following code illustrates how to plot a probability mass function for a Poisson distribution with lambda = 5:

#define range of "successes" success <- 0:20 #create plot of probability mass function plot(success, dpois(success, lambda=5), type='h')

The x-axis shows the number of “successes” – e.g. the number of events that occurred – 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 <- 0:20 plot(success, dpois(success, lambda=5), type='h', main='Poisson Distribution (lambda = 5)', ylab='Probability', xlab ='# Successes', lwd=3)

We 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 <- 0:20 #display probability of success for each number of trials dpois(success, lambda=5) [1] 0.0067379469991 0.0336897349954 0.0842243374886 0.1403738958143 [5] 0.1754673697679 0.1754673697679 0.1462228081399 0.1044448629571 [9] 0.0652780393482 0.0362655774156 0.0181327887078 0.0082421766854 [13] 0.0034342402856 0.0013208616483 0.0004717363030 0.0001572454343 [17] 0.0000491391982 0.0000144527054 0.0000040146404 0.0000010564843 [21] 0.0000002641211