A continuous probability distribution describes the probabilities of the possible values of a continuous random variable. Unlike discrete distributions, which deal with distinct and separate values, continuous distributions cover a range of values and are defined over intervals. The probability density function (PDF) is a key concept in continuous distributions, representing the likelihood of a random variable taking on a specific value.

One important aspect of continuous distributions is that the probability of the variable taking on any single, exact value is always zero. Instead, probabilities are determined over intervals. For example, if you have a uniform distribution over the interval ¹⁵, the probability of the variable being exactly 3 is zero, while the probability of it being between 2 and 4 can be calculated by finding the area under the curve of the PDF over that interval ¹.

Understanding continuous distributions is crucial in various fields, including statistics, data science, and machine learning, as they are often used to model real-world phenomena.