A Solution: Simulations

A.1 Solution Simulation - replacement

The option replace=TRUE activates sampling with replacement (i.e. the numbers that are picked are put back and can be picked again).

The option replace=FALSE activates sampling without replacement (i.e. the numbers that are picked are not put back and cannot be picked again).

Let’s try this out:

x <- c( 1, 2, 2, 3, 4, 1, 6, 7, 8, 10, 5, 5, 1, 4, 9 )

# Working example
sample(x, 10, replace = FALSE)

#>  [1] 4 5 2 1 1 4 7 8 1 2

# This will cause an error
sample(x, 20, replace = FALSE)

#> Error in sample.int(length(x), size, replace, prob): cannot take a sample larger than the population when 'replace = FALSE'

# Fix it
sample(x, 20, replace = TRUE)

#>  [1] 10  4  4 10  1  7  9  1  1  8  5  2  4  7 10  6  3  5
#> [19]  9  3

A.2 Solution Simulation - using sample

rolls_from_sample = sample(c(1:6), size=5000, replace=TRUE)
rolls_from_sample.int = sample(6, size=5000, replace=TRUE)

table(rolls_from_sample)

#> rolls_from_sample
#>   1   2   3   4   5   6 
#> 871 803 819 828 841 838

table(rolls_from_sample.int)

#> rolls_from_sample.int
#>   1   2   3   4   5   6 
#> 823 830 824 860 845 818

Both gives a uniform distribution over the numbers 1-6. The function sample.int is a specialised version of sample for sampling integers. Many R libraries have specialised versions of more general functions to do specific tasks under certain conditions.