7 Probability Functions

This chapter will primarily focus on the normal distribution functions in R.

7.1 Generating Random Numbers

To calculate random numbers in R based on a normal distribution, we can use the rnorm() function. By default, the mean and sd respectively are 0 and 1; but we can change these parameters as necessary.

set.seed(1) # Remember our random numbers
x <- rnorm(100,       # 100 random numbers
           mean = 50, # with a mean of 50
           sd = 20)   # and SD of 20.

plot(density(x),
     main = '100 Random Numbers')

See more on plots in the Graphing chapter.

7.2 Sampling

We can take a random sampling of a vector with sample().

set.seed(1) # Remember our random values.

# 10 random numbers from 
#   a vector of 100 values.
sample(1:100, size = 10, replace = TRUE)

##  [1] 68 39  1 34 87 43 14 82 59 51

For a dataset, we can do the following:

set.seed(1) # Remember our random values.

# Random 5 rows
mtcars[sample(1:NROW(mtcars), 5), ]

##                   mpg cyl disp  hp drat    wt  qsec vs am gear carb
## Pontiac Firebird 19.2   8  400 175 3.08 3.845 17.05  0  0    3    2
## Hornet 4 Drive   21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
## Duster 360       14.3   8  360 245 3.21 3.570 15.84  0  0    3    4
## Mazda RX4        21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag    21.0   6  160 110 3.90 2.875 17.02  0  1    4    4

7.3 Others

See ?rnorm, ?rchisq, and ?rpois for more information on normal, chi-square, and Poisson probability distributions

7.4 Summary

Table 7.1: Summary of Probability Distributions

Function	Description	Example
rnorm(x)	x random numbers based on a normal distribution.	rnorm(10)
sample(x, size)	Sample a vector with a specified size.	sample(1:100, size = 10)
Other probability functions.	See ?rnorm, ?rchisq, and ?rpois