What is Continuous Distribution?

Continuous uniform distribution is a probability distribution in which all outcomes are equally likely within a specified interval [a,b]. In other words, the probability density function (PDF) is constant over this interval, and the distribution is defined by the two parameters a and b, which are the lower and upper bounds, respectively.

In a continuous distribution:

• The total area under the probability density function (PDF) curve for a continuous distribution is equal to 1.
• Examples of continuous distributions include normal, uniform, and exponential distributions.

Example of Continuous Distribution

Examples of continuous uniform distribution are:

• Random Time of Day
• Random Position on a Line Segment
• Random Point in a Unit Square

Properties of Continuous Uniform Distribution

The properties of continuous uniform distribution are:

• Symmetry: The distribution is perfectly symmetric about the mean.

• Bell-shaped Curve: The shape of the normal distribution is often referred to as a “bell curve”.

• Mean, Median, and Mode: In a normal distribution, the mean, median, and mode are all equal and located at the center of the distribution.

Continuous and discrete uniform distributions are two types of probability distributions. A continuous uniform distribution has an interval of equally likely values. Instead, a discrete uniform distribution applies to a finite set of outcomes with equal probabilities.

In this article, we will discuss continuous and discrete uniform distribution along with a difference between them.