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Unit 4 - Introduction to Random Variables
Introduction to Statistics I (University of Calgary)
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Intro to Random Variables – 1
Unit 4: Introduction to Random Variables
Textbook: 4.1, 4.2, 4.3
Objectives
Know the definition of a random variable
Know the definition of a discrete random variable
Be able to construct and use a probability distribution table
Be able to sketch and/or interpret a probability distribution graph
Be able to calculate the expected value, variance, and standard deviation of a
random variable
Be able to calculate the expected value, variance, and standard deviation of a
linear transformation of a random variable
Motivation
To best introduce the concept of random variables in statistics, let’s briefly review how,
up until this point, we’ve been approaching probability calculations in class. We’ll go
back to a basic example from Unit 1.
Example
An experiment is performed in which two fair coins are tossed. The sample space of this
experiment is listed here:
HH HT TH TT
Let A be the event that we observe exactly 1 head. As we’ve learned in the previous
units, to calculate the probability of observing exactly 1 head, we calculate P(A) as
follows:
n(𝐀) 2 1
P(𝐀) = = =
n(𝐒) 4 2
In this particular case, we are interested in observing exactly 1 head. We defined this
outcome of interest as event A and calculate the probability of A occurring in any given
instance of the experiment.
Notice that we really don’t take into account the other possible outcomes of the
experiment. In other words, we don’t define an event for observing exactly 0 heads or
an event for observing exactly 2 heads. We just lump these other outcomes into AC, the
complement of the event we’re interested in.
Downloaded by Kelvin Mulimi ()
Unit 4 - Introduction to Random Variables
Introduction to Statistics I (University of Calgary)
Scan to open on Studocu
Studocu is not sponsored or endorsed by any college or university
Downloaded by Kelvin Mulimi ()
, lOMoARcPSD|56450245
Intro to Random Variables – 1
Unit 4: Introduction to Random Variables
Textbook: 4.1, 4.2, 4.3
Objectives
Know the definition of a random variable
Know the definition of a discrete random variable
Be able to construct and use a probability distribution table
Be able to sketch and/or interpret a probability distribution graph
Be able to calculate the expected value, variance, and standard deviation of a
random variable
Be able to calculate the expected value, variance, and standard deviation of a
linear transformation of a random variable
Motivation
To best introduce the concept of random variables in statistics, let’s briefly review how,
up until this point, we’ve been approaching probability calculations in class. We’ll go
back to a basic example from Unit 1.
Example
An experiment is performed in which two fair coins are tossed. The sample space of this
experiment is listed here:
HH HT TH TT
Let A be the event that we observe exactly 1 head. As we’ve learned in the previous
units, to calculate the probability of observing exactly 1 head, we calculate P(A) as
follows:
n(𝐀) 2 1
P(𝐀) = = =
n(𝐒) 4 2
In this particular case, we are interested in observing exactly 1 head. We defined this
outcome of interest as event A and calculate the probability of A occurring in any given
instance of the experiment.
Notice that we really don’t take into account the other possible outcomes of the
experiment. In other words, we don’t define an event for observing exactly 0 heads or
an event for observing exactly 2 heads. We just lump these other outcomes into AC, the
complement of the event we’re interested in.
Downloaded by Kelvin Mulimi ()
