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Chapter 4
Discrete Probability Distributions
It might seem paradoxical to say that uncertainty occurs in certain ways, but the truth is that it
does – assuming certain assumptions are satisfied. As we build a probability distribution,
whether in the form of a table or histogram, we can often times save ourselves a lot of labor by
focusing on the type of experiment that lay before us. The purpose of this chapter is to
(hopefully) simplify some of our efforts.
4.1 The Binomial Distribution
1.1.1 Why Probability Distributions Are Useful
Suppose a friend of yours, let‟s call him Kyle, tells you that his brother is 6-feet, 9-inches tall.
You are most likely wide-eyed and surprised by what he just told you.
Why is this
You likely have some idea of how tall people generally are. You would probably consider a
height of 6-feet, 9-inches to be uncommon in the environment you‟re used to. In fact, you might
even go as far as to call this height an outlier, or a value that falls outside the usual data range.
How can you be absolutely sure that this height is uncommon What if you live in a region that
tends to have shorter people
The statistician would say that it would be nice to see a probability distribution associated with
heights of all people living in the region, state, country, or continent on which you live. She
would argue that, if you are trying to describe the people in the U.S. based on people living in
Arizona, you are drawing from a biased sample.
While we will not discuss continuous random variables here (variables that can take on any
number in a specified range), we will show a theoretical distribution for heights in the U.S.
below:
Statistics for Decision-Making in Business © Milos Podmanik Page 146