Developing a Probability Distribution from Empirical Data
In real-world situations, statisticians obtain data by means of observation and experimental methods. Data obtained in this manner is called empirical data.
A probability distribution obtained by means of observation and experimental methods is referred to as an empirical probability distribution , or a relative frequency distribution based on observation.
Example:
Let X be the number of movies a high school student watches in a given month.
A survey conducted at one particular high school in the month of December gives by the following table:
If we assume that the students at this high school are typical, and that December is a typical month, then
The probability that a high school student will watch 1 movie per month is 17%;
The probability that a high school student will watch 2 movies per month is 28%;
etc.
Use this empirical probability distribution to find the expected value for the number of movies a high school student will watch in a month.
Convert the percentages to decimals.
17% = 0.17
Use the weighted average formula.
So, we can expect the average high school student to watch 2.95 movies per month.
