10.6. Discrete Distributions

Let us define our sample space:

> sample.space <- c(1,2,3, 4)

Let us define the probability mass function over the sample space:

> pmf <- c(0.25, 0.3, 0.35, 0.1)
> sum(pmf)
[1] 1

Let’s draw some samples from this distribution:

> sample(sample.space, size=10, replace=T, prob=pmf)
 [1] 2 3 3 3 3 4 2 1 3 2

Let’s tabulate them for large number of samples:

> table(sample(sample.space, size=10000, replace=T, prob=pmf))

   1    2    3    4
2578 3059 3383  980

Let’s verify their proportions:

> prop.table(table(sample(sample.space, size=10000, replace=T, prob=pmf)))

     1      2      3      4
0.2522 0.3029 0.3505 0.0944

Note that this matches quite well with the original probability mass function.