A Probability Density Function (PDF) is a mathematical function that describes the probability distribution of a continuous random variable. It assigns a density or relative likelihood to each possible value of the random variable.
A Probability Mass Function (PMF) is used to describe the probability distribution of a discrete random variable, while a PDF is used for continuous random variables. A PMF assigns a probability to each possible value, while a PDF assigns a density or relative likelihood to each possible value.
A PDF is used in statistics to calculate the probability of a continuous random variable falling within a specific range of values. It is also used to determine the mean, variance, and other statistical properties of a random variable.
A Cumulative Distribution Function (CDF) is the integral of a PDF and represents the probability that a random variable is less than or equal to a given value. In other words, the CDF is the sum of all the probabilities from the PDF up to a specific value.
The area under a PDF curve represents the probability of a continuous random variable falling within a certain range of values. The total area under the curve is equal to 1, meaning the probability of the random variable taking on any possible value is 1.