What are Continuous Probability Distributions (CPDs)?

A probability distribution is a mathematical function that describes the likelihood of different outcomes for a random variable. Continuous probability distributions (CPDs) are probability distributions that apply to continuous random variables. It describes events that can take on any value within a specific range, like the height of a person or the amount of time it takes to complete a task.

In continuous probability distributions, two key functions describe the likelihood of a variable taking on specific values:

Probability Density Function (PDF):

The PDF gives the probability density at a specific point or interval for a continuous random variable. It indicates how likely the variable is to fall within a small interval around a particular value.

• The height of the PDF curve at any point represents the probability density at that value.
• Higher density implies a higher probability of the variable taking on values around that point.

Cumulative Distribution Function (CDF):

The CDF gives the probability that a random variable is less than or equal to a specific value.It provides a cumulative view of the probability distribution, starting at 0 and increasing to 1 as the value of the random variable increases.

• The CDF starts at 0 for the smallest possible value of the random variable (since there is no probability below this value) and approaches 1 as the value approaches infinity (since the probability of the variable being less than or equal to infinity is 1).

CDF is the integral of the PDF, and the PDF is the derivative of the CDF.

Machine learning relies heavily on probability distributions because they offer a framework for comprehending the uncertainty and variability present in data. Specifically, for a given dataset, continuous probability distributions express the chance of witnessing continuous outcomes, like real numbers.