Chapter 6: Continuous Probability Distributions

A continuous random variable (usually denoted as X) is a variable that has an infinite number of random values in an interval of numbers. There are many different types of continuous distributions. To be a valid continuous distribution the total area under the curve has to be equal to one and the function’s y-values need to be positive.

For example, we may have a random variable that is uniformly distributed so we could use the Uniform distribution that looks like a rectangle. See Figure 6-1.

Uniform distribution graph: a horizontal blue segment at height 1/(b-a) spans between a and b, with dashed vertical lines dropping to open circles at a and b on the x-axis, outlining a rectangle.

Figure 6-1

We may want to model the time it takes customer service to complete a call with the exponential distribution. See Figure 6-2.

Three exponential distribution curves for mu = 4 in blue, mu = 1.2 in green, and mu = 0.5 in magenta over x from 0 to 10; the mu = 0.5 curve starts highest near 2 on the y-axis and drops fastest, while the mu = 4 curve starts lowest and decays slowest toward zero.

Figure 6-2

We may have standardized test scores that follow a bell-shaped curve like the Gaussian (Normal) Distribution. See Figure 6-3.

Adapted from Mostly Harmless Statistics by Rachel Webb (Portland State University, https://mostlyharmlessstat.wixsite.com/webpage), © Rachel Webb, licensed under CC BY-SA 4.0. Changes were made. License: CC-BY-SA-4.0.