3.2: The Probability Distribution
When we talk about the probability of discrete random variables, we normally talk about a probability distribution. In a probability distribution, you may have a table, a graph, or a chart that shows you all the possible values of
It is important to remember that the values of a discrete random variable are mutually exclusive. Think back to our car example with Jack and his mom. Jack could not, realistically, find a car that is both a Ford and a Mercedes (assuming he did not see a homebuilt car). He would either see a Ford or not see a Ford as he went from his car to the mall doors. Therefore, the values for the variable are mutually exclusive. Now let's look at an example.
Example 1
Say you are going to toss 2 coins. Show the probability distribution for this toss.
Solution:
Let the variable be the number of times your coin lands on tails. The table below lists all of the possible events that can occur from the tosses.
Toss  First Coin  Second Coin 


1  H  H  0 
2  H  T  1 
3  T  T  2 
4  T  H  1 
We can add a fifth column to the table above to show the probability of each of these events (the tossing of the 2 coins).
Toss  First Coin  Second Coin 



1  H  H  0 

2  H  T  1 

3  T  T  2 

4  T  H  1 

As you can see in the table, each event has an equally likely chance of occurring. You can see this by looking at the column
Now we can represent the probability distribution with a graph, called a histogram. A histogram is a graph that uses bars vertically arranged to display data. Using the TI84 PLUS calculator, we can draw the histogram to represent the data above. Let’s start by first adding the data into our lists. Below you will find the key sequence to perform this task. We will use this sequence frequently throughout the rest of this book, so make sure you follow along with your calculator.
This key sequence allows you to erase any data that may be entered into the lists already. Now let’s enter our data.
Now we can draw our histogram from the data we just entered.
The result is as follows:
We can see the values of
It's clear that the histogram shows the probability distribution for the discrete random variable. In other words,
Example 2
Does the following table represent the probability distribution for a discrete random variable?
Solution:
Yes, it does, since
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