Introduction to Discrete Random Variables
You can use probability and discrete random variables to calculate the likelihood of lightning striking the ground five times during a half-hour thunderstorm. (Credit: Leszek Leszczynski)A student takes a ten-question, true-false quiz. Because the student had such a busy schedule, he or she could not study and guesses randomly at each answer. What is the probability of the student passing the test with at least a
Small companies might be interested in the number of long-distance phone calls their employees make during the peak time of the day. Suppose the average is
These two examples illustrate two different types of probability problems involving discrete random variables. Recall that discrete data are data that you can count. A random variable describes the outcomes of a statistical experiment in words. The values of a random variable can vary with each repetition of an experiment.
Random Variable Notation
Upper case letters such as
For example, let
Activity
Toss a coin ten times and record the number of heads. After all members of the class have completed the experiment (tossed a coin ten times and counted the number of heads), fill in a table like the one below. Let| Frequency of |
Relative Frequency of |
|
|---|---|---|
- Which value(s) of occurred most frequently?
- If you tossed the coin times, what values couldtake on? Which value(s) ofdo you think would occur most frequently?
- What does the relative frequency column sum to?
Glossary
- Random Variable (RV)
- a characteristic of interest in a population being studied; common notation for variables are upper case Latin letters ,,,...; common notation for a specific value from the domain (set of all possible values of a variable) are lower case Latin lettersand. For example, ifis the number of children in a family, thenrepresents a specific integerVariables in statistics differ from variables in intermediate algebra in the two following ways.
- The domain of the random variable (RV) is not necessarily a numerical set; the domain may be expressed in words; for example, if = hair color then the domain is {black, blond, gray, green, orange}.
- We can tell what specific value the random variabletakes only after performing the experiment.
- The domain of the random variable (RV) is not necessarily a numerical set; the domain may be expressed in words; for example, if