http://www.ck12.org Chapter 3. Introduction to Discrete Random Variables
A(dependent events), and of eventAand eventBnot being affected by each other (independent events). We also
looked at examples where events cannot occur at the same time (mutually exclusive events), or when events were
not mutually exclusive and there was some overlap, so that we had to account for the double counting (mutually
inclusive events). If you recall, we used Venn Diagrams (below), tree diagrams, and even tables to help organize
information in order to simplify the mathematics for the probability calculations.
Our examination of probability, however, began with a look at the English language. Although there are a number of
differences in what terms mean in mathematics and English, there are a lot of similarities as well. We saw this with
the terms independent and dependent. In this and the following Concepts, we are going to learn about variables. In
particular, we are going to look at discrete random variables. When you see the sequence of wordsdiscrete random
variables, it may, at first, send a shiver down your spine, but let’s look at the words individually and see if we can
"simplify" the sequence!
The term discrete, in English, means to constitute a separate thing or to be related to unconnected parts. In
mathematics, we use the term discrete when we are talking about pieces of data that are not connected. Random, in
English, means to lack any plan or to be without any prearranged order. In mathematics, the definition is the same.
Random events are fair, meaning that there is no way to tell what outcome will occur. In the English language, the
term variable means to be likely to change or subject to variation. In mathematics, the term variable means to have
no fixed quantitative value.
Now that we have seen the 3 terms separately, let’s combine them and see if we can come up with a definition of a
discrete random variable. We can say that discrete variables have values that are unconnected to each other and have
variations within the values. Think about the last time you went to the mall. Suppose you were walking through the
parking lot and were recording how many cars were made by Ford. The variable is the number of Ford cars you see.
Therefore, since each car is either a Ford or it is not, the variable is discrete. Also,random variablesare simply
quantities that take on different values depending on chance, or probability. Thus, if you randomly selected 20 cars
from the parking lot and determined whether or not each was manufactured by Ford, you would then have a discrete
random variable.
Now let’s define discrete random variables.Discrete random variablesrepresent the number of distinct values that
can be counted of an event. For example, when Robert was randomly chosen from all the students in his classroom
and asked how many siblings there are in his family, he said that he has 6 sisters. Joanne picked a random bag of