Discrete random variables
• a random variable is a variable whose value is determined by the outcome of a
• a random variable that assumes countable values is called a discrete random
• a random variable that assumes any value contained in one or more intervals is
called a continuous random variable
Example: # fish in a lake; points scored in a football game; weight of a rhino;
Definition: the probability distribution of a discrete random variable, x, lists all
the possible values that the random variable can assume and their corresponding
Example: Suppose of 60% of all STATS151 students suffer from math anxiety.
Two students are randomly selected. Let x denote the number of students in the
sample who suffer from math anxiety. Construct the probability distribution of x.
Find : P(x >1) ; P(x 1); First student Second student Final outcomes
Y 0.6 YY=0.6*0.6=0.36
0.4 Y 4
Example: Space Shuttles. The National Aeronautics and Space Administration
(NASA) compiles data on space-shuttle launches and publishes them on its Web
site. The following table displays a frequency distribution for the number of crew
members on each shuttle mission from April 1981 to July 2000.
Let X denote the crew size of a randomly selected shuttle mission between April
1981 and July 2000.
a. What are the possible values of the random variable X?
b. Use random-variable notation to represent the event that the shuttle mission
obtained has a crew size of 7. c. Find P(X = 4); interpret in terms of percentages.
d. Obtain the probability distribution of X.
e. Construct a probability histogram for X.
Mean of a discrete random variable x is the value that is expected to occur per
repetition, i.e. on average if an experiment is repeated a large number of times.
μ = E(x) = ∑ xP(x)
σ = ∑ x P(x) − μ
Where is the standard deviation, measures the spread of the probability
distribution. Example: An instant lott