A mathematical function that describes the likelihood of various outcomes or events in a sample space. It provides a systematic way to assign probabilities to different events, allowing us to analyze and make predictions about uncertain situations.

There are different types of probability distributions, each with its own properties and applications. Here are a few commonly encountered distributions:

1. Discrete Probability Distribution: This type of distribution is used when the random variable takes on only discrete values. Examples include the Bernoulli distribution (for a single trial with two possible outcomes), the binomial distribution (for a fixed number of independent Bernoulli trials), and the Poisson distribution (for the number of events occurring in a fixed interval of time or space).
2. Continuous Probability Distribution: Continuous distributions are used when the random variable can take on any value within a certain range. The most well-known continuous distribution is the normal distribution (or Gaussian distribution), which is often used to model various phenomena in nature. Other important continuous distributions include the exponential distribution (for modeling the time between events in a Poisson process) and the uniform distribution (where all values in a range are equally likely).
3. Multivariate Probability Distribution: When dealing with multiple random variables, we use multivariate probability distributions. Examples include the multivariate normal distribution, which extends the concept of the normal distribution to multiple dimensions, and the multinomial distribution, which generalizes the binomial distribution to more than two outcomes.
4. Conditional Probability Distribution: In some situations, we may be interested in the probability distribution of one variable given the value of another variable. This is known as a conditional probability distribution. It can be represented as a function that gives the probability of one variable conditioned on the value of another variable.