Discrete Uniform Distribution
w/ 5+ Worked Examples!

What is a discrete uniform distribution?

It’s when all the distinct random variables have the exact same probability values, so everything is constant or just a number.

Let’s walk through has this works!

In a uniform probability distribution, all random variables have the same or uniform probability; thus, it is referred to as a discrete uniform distribution.

Imagine a box of 12 donuts sitting on the table, and you are asked to randomly select one donut without looking. Each of the 12 donuts has an equal chance of being selected. Therefore, the probability of any one donut being chosen is the same or uniform.

In fact, we can represent this idea using a simple graph as follows.

But notice that we can show this graphical representation as a density curve of a uniform distribution as a set of rectangles all having equal heights.

And, what’s important to note is that the value of the total area under any density curve equals one. Therefore, for a discrete uniform distribution, the probability mass function is

Moreover, if X is a uniform random variable for a is less than or equal to b, then the values of the mean and variance of a discrete uniform distribution is seen below. In addition, some additional derivations may be seen by Steven Wilson on MileFoot.

So, using our previous example of the box of 12 donuts, where you randomly select one donut without looking. Let’s identify the distribution and calculate it’s mean and variance.

In this video, we will use the properties of discrete uniform distributions to identify the probability mass function along with the mean and variance.

Discrete Uniform Distribution – Lesson & Examples (Video)

21 min

• Introduction to Video: Discrete Uniform Distributions
• 00:00:36 – How to create, identify and graph a discrete uniform distribution? (Examples #1-2)
• Exclusive Content for Members Only

• 00:05:59 – Formulas for finding the mean and variance of a discrete uniform distribution (Example #3)
• 00:11:44 – Write the uniform distribution and find the mean and variance (Example #4)
• 00:14:13 – Find the mean and variance given the range of a distinct uniform random variable (Example #5)
• 00:15:59 – Find the expected value and variance of X for the random variable (Example #6a)
• 00:17:31 – Determine the mean and variance after the transformation of uniform random variable (Example #6b)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions