## Introduction

Probability distribution is a statistical function that describes the likelihood of obtaining different outcomes from a random experiment or process. It specifies the possible values that a random variable can take and the probability of each value occurring.

## What is Probability Distribution?

A probability distribution is a mathematical function that describes the likelihood of different outcomes in a random experiment or event. Probability distributions can be either discrete or continuous. A discrete probability distribution describes the probability of each possible outcome of a discrete random variable, which takes on a finite or countably infinite set of possible values.

**For example,** the probability distribution of the outcome of rolling a fair six-sided die is a discrete uniform distribution, where each outcome has an equal probability of 1/6.

## Types of Probability Distribution

There are two types of probability distributions: discrete and continuous.

## 1. Discrete Probability Distribution

A discrete probability distribution is one in which the possible values of the random variable are countable and finite or infinite.** Examples of discrete probability distributions** include the binomial distribution, Poisson distribution, and geometric distribution.

**Binomial Distribution:**The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials. The probability of success in each trial is denoted by p, and the probability of failure is denoted by q = 1 – p. The binomial distribution has two parameters: n, the number of trials, and p, the probability of success.**Poisson Distribution:**The Poisson distribution is a discrete probability distribution that describes the number of occurrences of an event in a fixed interval of time or space. The Poisson distribution has one parameter: λ, the average rate of occurrence.**Geometric Distribution:**The geometric distribution is a discrete probability distribution that describes the number of trials needed to obtain the first success in a series of independent trials. The probability of success in each trial is denoted by p, and the probability of failure is denoted by q = 1 – p. The geometric distribution has one parameter: p, the probability of success.

## 2. Continuous Probability Distribution

A continuous probability distribution is one in which the possible values of the random variable are uncountable and infinite. **Examples of continuous probability distributions** include the normal distribution, exponential distribution, and uniform distribution.

**Normal Distribution:**The normal distribution is commonly used in statistics to model many natural phenomena. The normal distribution is characterized by two parameters: μ, the mean, and σ, the standard deviation.**Exponential Distribution:**The exponential distribution is a continuous probability distribution that describes the time between occurrences of a random event. The exponential distribution has one parameter: λ, the rate parameter.**Uniform Distribution:**The uniform distribution is a continuous probability distribution in which all values within a given range are equally likely to occur. The uniform distribution has two parameters: a, the lower bound, and b, the upper bound.