Continuous Uniform Distribution
Defined w/ 5 Examples!

Did you know that the simplest of all continuous probability distributions is the Continuous Uniform Distribution?

In a continuous uniform distribution, sometimes called a rectangular distribution, the density function is constant, or flat, where every variable has an equal chance of occurring as noted on the Engineering Statistics Handbook.

And as we know that the total area under all density curves is one, we can easily calculate this using our geometry knowledge.

To put it more succinctly, the data collected shows that the probability of outcome occurring is the same number; hence, forming a rectangle whose height is the value of likelihood.

Alright, now let’s look at a real-life example.

Imagine you live in a building that has an elevator that will take you to your floor. From experience, once you push the button to call the elevator, it takes between ten and thirty seconds for you to arrive at your floor. This means the elevator arrival is uniformly distributed between 10 and 30 seconds once you hit the button.

So, if X is a continuous uniform random variable has probability density function mean, and variance is as follows.

Now, using our previous example of the box of riding the elevator, let’s identify the rectangular distribution density function and calculate its mean and variance.

This means that you should expect the elevator to take 20 seconds to arrive at your floor with a standard error of 5.774 seconds.

This video will use the properties of continuous uniform distributions to identify the probability density function along with the mean and variance and use these formulas to calculate probability.

Continuous Uniform Distribution – Lesson & Examples (Video)

59 min

• Introduction to Video: Continuous Uniform Distribution
• 00:00:34 – Properties of a continuous uniform Distribution with Example #1
• Exclusive Content for Members Only

• 00:13:35 – Find the probability, mean, and standard deviation of a continuous uniform distribution (Examples #2-3)
• 00:27:12 – Find the mean and variance (Example #4a)
• 00:30:01 – Determine the cumulative distribution function of the continuous uniform random variable (Example #4b)
• 00:34:02 – Find the probability (Example #4c)
• 00:36:08 – Prove the formula for the mean of a continuous uniform distribution (Example #5a)
• 00:39:28 – Verify the formula for variance (Example #5b)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions