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Math 160
Intro to Statistics
OCC
Section 5.1 – Discrete Random Variables and Probability Distributions
Random Variable
A random variable is a quantitative variable whose value depends on chance.
Discrete Random Variable
A discrete random variable is a random variable whose possible values can be listed.
Probability Distribution
A listing of possible values and corresponding probabilities of a discrete random variable, or a formula for the
probabilities.
Probability Histogram
A graph of the probability distribution that displays the possible values of a discrete random variable on the
horizontal axis and the probabilities of those values on the vertical axis. The probability of each value is
represented by a vertical bar whose height equals the probability.
Sum of the Probabilities of a Discrete Random Variable
For any discrete random variable X, we have  P( X  x)  1 .
[Note: P( X  x) can also be written as P( x) ].
Interpretation of a Probability Distribution
In a large number of independent observations of a random variable X, the proportion of times each possible
event occurs will approximate the probability of X; or, equivalently, the proportion histogram will approximate
the probability histogram for X.
 Exercises:
1)
Class Activity: The data will be collected by each member of the class. Each student will write on
the board, the total number of natural siblings they have. Let the random variable X represent the
number of siblings each student has.
a)
Draw a probability distribution for the random variable X.
b)
What are the possible values that the
random variable X can take on?
c)
Find P( X  2) or P(2) .
d)
Find P( X  3) .
e)
Find P( X  2) .
f)
Find P(4  X  6) .
X
P(X = x)
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