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In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. In more technical terms, the probability distribution is a description of a random phenomenon in terms of the probabilities of events. For instance, if the random variable X is used to denote the outcome of a coin toss, then the probability distribution of X would take the value 0.5 for X = heads, and 0.5 for X = tails. Examples of random phenomena can include the results of an experiment or survey.

### Introduction

### Terminology

### Cumulative distribution function

### Discrete probability distribution

### Continuous probability distribution

### Some properties

### Andrey Kolmogorov

### Random number generation

### Common probability distributions and their applications