3.1. Discrete Random Variables http://www.ck12.org
jelly beans at the store, and only 15 of 250 jelly beans were green. When randomly selecting from the most popular
movies, Jillian found thatIron Man 2grossed 3.5 million dollars in sales on its opening weekend. Jack, walking
with his mom through the parking lot, randomly selected 10 cars on his way up to the mall entrance and found that
only 2 were Ford vehicles.
The probability of a discrete random variable can range anywhere from 0 to 1. The less likely a discrete random
variable is to occur, the closer the probability will be to 0, and the more likely a discrete random variable is to occur,
the closer the probability will be to 1.
Example A
Which of the following can be represented by a discrete random variable?
a. The heights of the students in a high school
b. The number of sit-ups that you can do
c. The distances between stars in a galaxy
d. The number of wins by a professional hockey team
e. The speeds of the cars in a race
The heights of the students in a high school cannot be represented by a discrete random variable, since a height
can take on any value within a certain range. For example, a height could be 64 inches, 64.5 inches, 64.55 inches,
64.555 inches, and so on. On the other hand, the number of sit-ups that you can do can be represented by a discrete
random variable, because the number will always be an integer. The distances between stars in a galaxy are similar
to the heights of the students in a high school in that there are an infinite number of possibilities, so these distances
cannot be represented by a discrete random variable. However, the number of wins by a professional hockey team is
similar to the number of sit-ups that you can do in that the number will always be an integer, so this number can be
represented by a discrete random variable. Finally, the speeds of the cars in a race can take on any values, such as
100 MPH, 100.1 MPH, 100.12 MPH, 100.123 MPH, and so on, so these speeds cannot be represented by a discrete
random variable. In summary, the answers to this question are as follows:
a. Cannot be represented by a discrete random variable
b. Can be represented by a discrete random variable
c. Cannot be represented by a discrete random variable
d. Can be represented by a discrete random variable
e. Cannot be represented by a discrete random variable
Example B
It is very likely, but not certain, that the high temperature will exceed 75◦F every day next week. Suppose that the
discrete random variableXrepresents the number of days next week that the high temperature will exceed 75◦F.
Which of these could beP(X= 7 )?
a.P(X= 7 ) = 0
b.P(X= 7 ) = 0. 14
c.P(X= 7 ) = 0. 5
d.P(X= 7 ) = 0. 96
e.P(X= 7 ) = 1
If the probability of an event is 0, it is impossible, and if the probability of the event is 1, it is certain. In this case,