Lesson 6: Random Variables
Learning objectives for this lesson
Upon completion of this lesson, you should be able to:
•
distinguish between discrete and continuous random variables
•
find probabilities associated with a discrete probability distribution
•
compute the mean and variance of a discrete probability distribution
•
find probabilities associated with a binomial distribution
Random Variables
A
random variable
is numerical characteristic of each event in a sample space, or
equivalently, each individual in a population.
Examples:
•
The number of heads in four flips of a coin (a numerical property of
each different sequence of flips).
•
Heights of individuals in a large population.
Random variables are classified into two broad types
•
A
discrete random variable
has a countable set of distinct possible
values.
•
A
continuous random variable
is such that any value (to any number
of decimal places) within some interval is a possible value.
Examples of discrete random variable:
•
Number of heads in 4 flips of a coin (possible outcomes are 0, 1, 2, 3,
4).
•
Number of classes missed last week (possible outcomes are 0, 1, 2,
3,
, up to some maximum number)
•
Amount won or lost when betting $1 on the Pennsylvania Daily
number lottery
Examples of continuous random variables:
•
Heights of individuals
•
Time to finish a test
•
Hours spent exercising last week.
Note
: In practice, we don't measure accurately enough to truly see all possible values
of a continuous random variable. For instance, in reality somebody may have
exercised 4.2341567 hours last week but they probably would round off to 4.
Nevertheless, hours of exercise last week is inherently a continuous random variable.
Probability Distributions
For a discrete random variable, its
probability distribution
(also called the
probability distribution function) is any table, graph, or formula that gives each
possible value and the probability of that value.
Note
: The total of all probabilities
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View Full Documentacross the distribution must be 1, and each individual probability must be between 0
and 1, inclusive.
Examples:
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 Spring '08
 BARROSO,JOAOR
 Statistics, Probability, Probability theory, $2, $20, Pennsylvania, $0.17

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