Continuous Distributions

This is an introduction to the probability functions of continuous random variables, from a post-secondary perspective. One of the most fundamental functions of this type is the normal distribution. Since it has been covered elsewhere, our main focus is on another fundamental continuous probability function, the uniform distribution.

We close this essay by considering one of the simplest of all continuous distributions; the uniform distribution. Let U be a Uniform random variable defined on the interval (a, b). Then the pdf of U is:

We express that U is a Uniform random variable by writing:

The distribution U(0,1) frequently arises in applications.

The cumulative distribution function (cdf) of U(a,b) is:

If X is U(a,b), the mean of X is:

Also, the variance of X ~U(a,b) is: