MATH 335: Using R to simulate continuous probability functions.

R has built in functions to randomly generate sequences of independent observations from various "standard" probability distributions. Here we will look at the uniform.

The R function runif generates from the uniform. To get a full description type:

help(runif)

The general form is runif(n, min=0, max=1), where n is a non-optional argument specifying how many observations you want and min and max specify the endpoints; these arguments have default values of 0 and 1, resp.

In class we did the following experiment. (Note that anything after the # symbol is a comment that R ignores.)

x <- runif(100) # generate the numbers
x # look at the numbers
sort(x) # look at the numbers in increasing order
hist(x) # see a histogram of the numbers

We learned that you can see such a histogram in one fell swoop by: hist(runif(100))

We had some uproarious fun by using the up-arrow key and key to repeat this experiment in rapid-fire succession to see the variability in taking samples repeatedly.

If you typed:

hist(runif(100,20,100))

You would get a similar experience, except that your random numbers would be between 20 and 100 instead of 0 and 1.

Here is a list of other "standard" probability functions that R makes available.

Distribution		R name

beta			beta
binomial		binom
Cauchy			cauchy
chi-squared		chisq
exponential		exp
F			f
gamma			gamma
geometric		geom
hypergeometric		hyper
log-normal		lnorm
logistic		logis
negative binomial	nbinom
normal			norm
Poisson			pois
Student's t		t
uniform			unif
Weibull			weibull
Wilcoxon		wilcox