[For Windows users, select the "base" package, and then download and run the ".exe" install file.]

**Simple arithmetic**
may be done directly, including simple expressions like:

3 + 4or more complicated expressions like:

3.7 + 11 * exp(2) - 17^2 + sqrt(5) / 3

w = 7.2Alternatively, the "=" may be replaced by "<-" (i.e. "less-than" followed by "dash"), as in "w <- 7.2".

**Lists**
of data may be entered directly using the "c( )" function, for example:

x = c(2, 4, 1.7, -3)Once this is done, then typing just "x" will output x as a list (i.e. vector). Or, typing e.g. "x[3]" will output the 3rd element, 1.7. Also "length(x)" is 4, so e.g. "x[length(x)]" will output -3.

Once x is a list, then its **sum**, **mean**
(x-bar), **variance** (s^2), **standard
deviation** (s), etc. can be computed directly:

sum(x)[Of course, "sd(x)" is the same as "sqrt(var(x))".] If you wish, you can assign these values to other variables, e.g. "mu = mean(x)", "s = sd(x)", etc.

mean(x)

var(x)

sd(x)

Lists can themselves be operated on. In the example above, "x^2" would produce the list (4, 16, 2.89, 9), so that e.g. "mean(x^2)" would give 7.9725. Equivalently, you could first do "z = x^2", and then "mean(z)" would also be 7.9725.

When typing commands in R, you can use the up-arrow key to retrieve
**previous commands**, and the left-arrow key to
**edit** a command that you've already typed.

R can also **generate pseudorandom values**.
For example, to generate 50 i.i.d. draws from a standard normal
distribution, type "rnorm(50)". To save them as a list called "y", type
"y = rnorm(50)". Then you can compute their mean etc. by "mean(y)",
"var(y)", "sd(y)", etc.

To generate from other distributions, use e.g. "rbinom(50, 10, 0.3)" for the Binomial(10, 0.3) distribution, "rpois(50, 14)" for the Poisson(14), "runif(10, 2, 4)" for Uniform[2,4], "rexp(50, 0.3)" for Exponential(0.3), etc. To compute cdf's, use e.g. "pnorm(1.2)" for the standard normal, "pexp(1.2, 0.3)" for Exponential(0.3), "pchisq(74.22, 100)" for the chisquared(100) distribution, "pt(2.228, 10)" for the t(10) distribution, "pf(5.7, 2, 10)" for the F(2, 10) distribution, etc.; for densities use "dnorm(1.2)", "dexp(1.2, 0.3)", etc.

R also has excellent **plotting** features. For example,
"plot(x)" will plot the individual values of x above, while "hist(x)"
will display a histogram. Also, "pie(x^2)" will display a pie-chart of
x^2 (or any other non-negative list). Try them! [If you prefer, you
can save your plot as a pdf file, by typing "pdf()", then "plot(x)" (or
whatever), and then "dev.off()". If you want a jpeg or postscript
file instead of pdf, then type "jpeg()" or "postscript()" instead of "pdf()".]

Once you have typed "y = rnorm(50)", then you can e.g. get a histogram of this sample by typing

hist(y)To then e.g. get a second histogram, of a fresh sample, overlaid on the first, in a different colour, you could type

hist(rnorm(50), add=TRUE, border=2)

**Longer sequences of R commands** (e.g. full
**computer programs**) can be saved to a file, and then
executed by typing

source("filename")

The number sign # indicates a **comment** (useful for
explaining what you are doing); everything from # to the end of the line
is ignored by R.

**When you are done** with your computations, type "q()"
to quit R.

There is
lots of **documentation** about R available on the web, see e.g.
here or here or here
or here.

In addition, R has lots of **built-in help** available.
For example, to find out more about the "hist" function, simply type
"help(hist)" or "?hist" after the R prompt. Or, for an interactive
R-help web interface, type "help.start()".
There is lots to read and try and investigate and use -- have fun!

-- Jeffrey S. Rosenthal, Department of Statistics, University of Toronto