A commonly observed type of distribution among continuous variables is a **uniform distribution**. For a continuous random variable following a uniform distribution, the value of probability density is equal for all possible values. Let’s explore this distribution a little more.

Since all possible values are between 0 and 10, the area under the curve between 0 and 10 is equal to 1.

Clearly, this area is the area of a rectangle with length 10 and unknown height h. Hence, you can say that 10 * h = 1, which gives us h = 0.1. So, the value of the PDF for all values between 0 and 10 is 0.1.

The cumulative probability for X = 0.5 is equal to the area under the curve between X = 0, the lowest possible value, and X = 0.5.

This area = 0.1 * 0.5 = 0.05.

Now you must be wondering when to use PDFs and when to use CDFs. They are both good for continuous variables, but which one is used more in real-life analyses?

Well, PDFs are more commonly used in real life. The reason is that it is much **easier to see patterns in PDFs** as compared to CDFs. For example, here are the PDF and the CDF of a uniformly distributed continuous random variable:

The **PDF clearly shows uniformity**, as the probability density’s value remains constant for all possible values. However, the **CDF does not show any trends** that help you identify quickly that the variable is uniformly distributed.

Now, let’s look at the PDF and the CDF of a symmetrically distributed continuous random variable:

Again, it is clear that the symmetrical nature of the variable is much more apparent in the PDF than in the CDF.

Hence, generally, PDFs are used more commonly that CDFs.