Rolling Two Dice Random Variables Using R
Stat 341 - Fall 2008
In some examples, the sample space of the experiment is small enough to easily use R to study
the distribution of the random variables arising from the particular sample space. In this help file,
we will look at R code for the sample space of rolling two dice. The sample space consists of 36
simple events, each having the same probability 1/36. The following R code will set up the sample
space S in a matrix with two columns (the outcomes on the two dice) and 36 rows (the 36 possible
outcomes).
Stwodice<- scan()
111213141516
212223242526
313233343536
414243444546
515253545556
616263646566
Stwodice<- matrix(Stwodice, byrow = T, ncol = 2)
Applying the sum function or the max function to the rows of this matrix will produce the 36
sums and 36 maximum values corresponding to the 36 simple events in S.
sumtwodice<- apply(Stwodice, 1, sum)
maxtwodice<- apply(Stwodice, 1, max)
We can then study the distribution of the two random variables using histograms and summary
statistics. For example, to find the smallest and largest possible values of the sums, you can type
min(sumtwodice)
max(sumtwodice)
To find other summary statistics of the possible sums, like the mean, median, five number summary,
and standard deviation, you can type
mean(sumtwodice) #mean
sqrt(var(sumtwodice)) #std. dev.
fivenum(sumtwodice) #five number summary
To get a picture of the distribution of the possible sums, you can make a probability histogram.
For these values, you should set up the histogram so that the possible values are centered in the
bars of the histogram. For example, for the sums, you should set up your histogram as
sumdicebreaks<- c(1:12) + 0.5
hist(sumtwodice, breaks = sumdicebreaks, prob = T)
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