http://www.ck12.org Chapter 3. Discrete Random Variables - Basic
3.1 Discrete Random Variables
Learning Objectives
- Demonstrate an understanding of the notion of discrete random variables by using them to solve for the
probabilities of outcomes, such as the probability of the occurrence of five heads in 14 coin tosses.
You are in statistics class. Your teacher asks what the probability is of obtaining five heads if you were to toss 14
coins.
(a) Determine the theoretical probability for the teacher.
(b) Use the TI calculator to determine the actual probability for a trial experiment for 20 trials.
Work through Chapter 3 and then revisit this problem to find the solution.
Whenever you run and experiment, flip a coin, roll a die, pick a card, you assign a number to represent the value to
the outcome that you get. This number that you assign is called arandom variable. For example, if you were to
roll two dice and asked what the sum of the two dice might be, you would design the following table of numerical
values.
These numerical values represent the possible outcomes of the rolling of two dice and summing of the result. In
other words, rolling one die and seeing a 6 while rolling a second die and seeing a 4. Adding these values gives you
a ten.
The rolling of a die is interesting because there are only a certain number of possible outcomes that you can get
when you roll a typical die. In other words, a typical die has the numbers 1, 2, 3, 4, 5, and 6 on it and nothing else.
Adiscrete random variablecan only have a specific (or finite) number of numerical values.
A random variable is simply the rule that assigns the number to the outcome. For our example above, there are 36
possible combinations of the two dice being rolled. The discrete random variables (or values) in our sample are 2,
3, 4, 5, 6, 7, 8, 9, 10, 11, and 12, as you can see in the table below.