Chapter 6
Inferential Statistics
We shall assume that the student has had some previous exposure to
elementary probability theory; here we’ll just gather together some rec-
ollections.
The most important notion is that of a random variable; while
we won’t give a formal definition here we can still convey enough of its
root meaning to engage in useful discussions. Suppose that we are to
perform an experiment whose outcome is a numerical valueX. That
X is a variable follows from the fact that repeated experiments are
unlikely to produce the same value ofXeach time. For example, if we
are to toss a coin and let
X =
1 if heads,
0 if tails,then we have a random variable. Notice that this variableXdoes not
have a value until after the experiment has been performed!
The above is a good example of a discrete random variable in
that there are only two possible values ofX: X = 0 andX = 1. By
contrast, consider the experiment in which I throw at dart at a two-
dimensional target and letX measure the distance of the dart to the
center (bull’s eye). Here,X is still random (it depends on the throw),
but can take on a whole continuum of values. Thus, in this case we call
Xacontinuous random variable.
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