Here's what you'll find in this section:
In an experiment, each outcome can be associated with a single number by using a rule of association, or random variable. By converting outcomes to numbers, we can use mathematics to give us insight into the experiment or study being conducted.
NOTE:\ We usually denote random variables with capital letters, e.g., the random variables X or Y.
EXAMPLE:\ Consider the following random variables:
NOTE: (Properties of E): Let a and b be real constants, then
A shortcut formula for the variance, which is usually easier to evaluate then the definition formula, is
or in symbols,
NOTE: (Properties of ): Let a and b be real constants, then
EXAMPLE:\ At a certain country market, the probabilities (long-run frequencies) for the number of apples bought by customers was tabulated:
The expected value of the number of apples purchased is
Its variance is computed in two stages: first we calculate as follows,
and then we apply the formula for the variance
The standard deviation of X is obtained by .
NOTE:\ The expected value of a random variable X is just a weighted average of the values of X, where the weights are the associated probabilities (or relative frequencies).
The webmaster and author of this Math Help site is Graeme McRae.