Rolling Two Dice Examples Using R
Stat 341 - Fall 2008
This is the R code that looks at two different random variables obtained from the sample space of
the experiment of rolling two 6-sided dice: the sum of the values on the two dice and the largest
or maximum value of the two dice. Using R, we will study the observed probability distributions
of these random variables.
To begin, we need to create a virtual dice in R. The code is
dice<- c(1:6)
We would then like to roll the dice twice and observe the outcome and then repeat the process
10,000 times. The R code to do this is
dice1<- sample(dice,10000,replace = T)
dice2<- sample(dice,10000,replace = T)
No we have 10000 rolls of our two dice in the variables dice1 and dice2. But they are in separate
variables and we need to join them together into a matrix. Each dice will become a column in the
matrix and each roll of the 2 dice will become a row in the matrix. Here is the R code to do this.
dicematrix<- cbind(dice1,dice2)
At this point, it may be helpful to look at the matrix dicematrix. To look at the first 20 rows,
type in the command
dicematrix[1:20,]
Now we would like to look at the values in each row (the outcomes of the rolls of our 2 dice) and
calculate the sum of the two dice and the largest or maximum of the two dice. In R, whenever
you have a matrix, you can apply a mathematical function (like sum) to each row or column of the
matrix with the same command. In this case, we would like to apply two different functions (sum
and max) to each of our 10000 rows of the matrix dicematrix. The commands are
sumtwodicesim<- apply(dicematrix,1,sum)
maxtwodicesim<- apply(dicematrix,1,max)
In the commands above, the first value is the name of the matrix, the second value of 1 specifies
we want to apply the function to the rows and the third value is the name of the function we want
to apply.
We can then study the 10000 observed values of these two random variables using histograms and
summary statistics. For example, to find the smallest and largest values of the observed sums, you
can type
min(sumtwodicesim)
max(sumtwodicesim)
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