Random Variables and Probability Distributions
This section first defines discrete and continuous random variables. Then, it introduces the distributions for discrete random variables. It also talks about the mean and variance calculations.
- To learn the concept of a random variable.
- To learn the distinction between discrete and continuous random variables.
A random variable is a numerical quantity that is generated by a random experiment.
We will denote random variables by capital letters, such asor , and the actual values that they can take by lowercase letters, such as and .
Table 4.1 "Four Random Variables" gives four examples of random variables. In the second example, the three dots indicates that every counting number is a possible value for .
Table 4.1 Four Random Variables
|Possible Values of
|Roll two fair dice
|Sum of the number of dots on the top faces
|2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
|Flip a fair coin repeatedly
|Number of tosses until the coin lands heads
|1, 2, 3,4, …
|Measure the voltage at an electrical outlet
|118 ≤≤ 122
|Operate a light bulb until it burns out
|Time until the bulb burns out
|0 ≤< ∞
A random variable is called discrete if it has either a finite or a countable number of possible values. A random variable is called continuous if its possible values contain a whole interval of numbers.
The examples in the table are typical in that discrete random variables typically arise from a counting process, whereas continuous random variables typically arise from a measurement.
This text was adapted by Saylor Academy under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License without attribution as requested by the work's original creator or licensor.