Topics: Probability - Distribution Function


Let be an absolutely continuous random variable such that , where all intervals of a given length have the same probability.

In such a case, we say that has a continuous uniform distribution (or rectangular distribution) and write .

Density Function


The density function of such an is given by:

Distribution Function


Such an ’s distribution function is:

Expected Value


When it comes to the expected value of such an , it is:



As for the variance of such an , it is:

Moment-Generating Function


The moment-generating function of such an is: