http://www.ck12.org Chapter 4. Discrete Probability Distribution
4.1 Two Types of Random Variables
Learning Objectives
- Learn to distinguish between the two types of random variables: continuous and discrete.
The word discrete means countable. For example, the number of students in a class is countable or discrete. The
value could be 2, 24 , 34 ,or 135 students but it cannot be 232/3 or 12.23 students. The cost of a loaf of bread is also
discrete, say $3.17, where we are counting dollars and cents, but not fractions of a cent.
However, if we are measuring the tire pressure in an automobile, we are dealing with a continuous variable. The air
pressure can take values from 0 psi to some large amount that would cause the tire to burst. Another example is the
height of your fellow students in your classroom. The values could be anywhere from, say, 4.5 feet to 7.2 feet. In
general, quantities such as pressure, height, mass, weight, density, volume, temperature, and distance are examples
of continuous variables. Discrete random variables come usually from counting, say, the number of chickens in a
coop, or the number of passing scores on an exam or the number of voters who showed up to the polls.
One way of distinguishing discrete and continuous variables is between any two values of a continuous variable,
there are an infinite number of other valid values. This is not the case for discrete variables; between any two
discrete values, there are an integer number( 0 , 1 , 2 ,...)of valid values. For a discrete variable, these are considered
countablevalues since you could count a whole number of them.
Discrete Random Variables and Continuous Random Variables
Random variables that assume acountable number of valuesare called discrete.
Random variables that can take any of thecountless number of valuesare called continuous.
Example:
Here is a list of discrete random variables:
- The number of cars sold by a car dealer in one month:x= 0 , 1 , 2 , 3 ,...
- The number of students who were protesting the tuition increase last semester:x= 0 , 1 , 2 , 3 ,....Notice thatx
could become very large. - The number of applicants who have applied for the vacant position at a company:x= 0 , 1 , 2 , 3 ,...
- The number of typographical errors in a rough draft of a book:x= 0 , 1 , 2 , 3 ,...
Example:
Here is a list of continuous random variables:
- The length of time it took the truck driver to go from New York city to Miami:x>0, wherexis the time.
- The depth of oil drilling to find oil: 0<x<c, wherecis the maximum depth possible.
- The weight of a truck in a truck weighing station: 0<x<c, wherecis the maximum weight possible.
- The amount of water loaded in a 12−ounce bottle in a bottle filling operation: 0<x< 12.