4.1. Standard Distributions http://www.ck12.org
Notice, the exponential distribution curve is also showing continuous data but the graph is curved and not straight.
Therefore, anexponential distributionis a probability distribution showing the relation in the formy=axwherea
is any positive number.
Let’s look at our example from the start of the chapter.
Say you were buying a new bicycle for going back and forth to school. You want to buy something that lasts a long
time and something with parts that will also last a long time. You research on the internet and find one brand “Buy
Me Bike” that shows the following graph with all of its advertising.
(a) What type of probability distribution is being represented by this graph?
(b) Is the data represented continuous or discrete? How can you tell?
(c) Does the data in the graph indicate that the company produces bicycles that have a respectable life span? Explain.
Solution:
(a) The distribution in this graph is exponential because it is a curved plot of data.
(b) The data is continuous because the data points are joined together. Discrete data points would not be joined
together.
(c) In the graph, the parts will last for many years before breaking down. At 20 years, for example, the age of the
parts is still equals 0.15 years.