Random Numbers and Random Lists

Random Integers

Using R we can generate either a single random integer, or a list of random integers. To do this we need to decide how many random numbers we want, the upper and lower bounds for our selections, and whether we want our selections to occur with or without replacement.

Example: Generate a single random integer between 1 and 10.

> sample(1:10, 1)
[1] 4

Every time we repeat this command a different random integer will be selected.  We can also store a random  integer as a variable for use in our calculations.

Example: Generate a single random integer between 1 and 10, and store this number as x1.  Then calculate 3*x1.

> x1 = sample(1:10, 1)
> x1
[1] 10

Now that we have created the variable x1, we can all on it at any time to include it in a calculation.

> 3 * x1
[1] 30

Example: Generate a list of 15 randomly selected integers between 0 and 20, chosen without replacement.

Let's call this list rand.int.  The default option for the sample command is to select values without replacement.

> rand.int = sample(1:20, 15)
> rand.int
[1]  6  2 16  8  9  5 18 14 15 11 10 19 12  3  1

By storing these 10 randomly selected integers as a list, we can call on them for future calculations.

Example: Generate a list of 15 randomly selected integers between 0 and 20, chosen with replacement.

Let's call this list rand.int.2.  The default option for the sample command is to select values without replacement, so we will have to include the argument replace = TRUE.

> rand.int.2 = sample(1:20, 15, replace = TRUE)
> rand.int.2
[1] 17  7 17  1 10 20 16 20 10 18 10 16 12 17 15

Again, we now have a list of random integers we can call on for future calculations.

Random Real Numbers

The runif command is used to select random real numbers from the uniform distribution.  We can choose to generate one or more random numbers between any upper and lower bounds.

Example: Generate a single random number between 2.2 and 3.5.

> runif(1, 2.2, 3.5)
[1] 3.305643

As with random integers, we could also store this number as a variable for use in later calculations.

Example: Generate a list of 10 randomly selected numbers between 1.75 and 10.82.

> runif(10, 1.75, 10.82)
[1] 8.261552 8.159828 2.909501 8.097809 5.041455 9.397430 8.381366 9.432151
[9] 6.813843 6.762412

The [1] at the beginning of the first line indicates this is the first value in our list.  The [9] at the beginning of the second line indicates this is the ninth value in our list.

This list could also be stored, and called upon for later calculations.

Normal Random Numbers

The rnorm command is used to select random real numbers from the normal distribution.  We can choose to generate one or more random numbers with a specified mean and standard deviation.

Example: Generate a single random number from the standard normal distribution.

For the standard normal distribution μ = 0 and σ = 1.  These are the default values for the rnorm command.

> rnorm(1)
[1] 1.201658

Example: Generate a list of 5 randomly selected numbers from the standard normal distribution.

> rnorm(5)
[1] -0.1209757  0.6925115 -0.6782760 -0.1545111  0.4656249

Example: Generate a list of 5 randomly selected numbers from a normal distribution with a mean of 15 and standard deviation of 3.2.

We will now need to add additional arguments to set μ = 15 and σ = 3.2.

> rnorm(5, mean = 15, sd = 3.2)
[1] 10.43209 14.11475 18.60285 13.46017 14.58410

These values and lists could also be stored, and called upon for later calculations.