# Probability Distribution

Understanding**statistical distributions**is fundamental for researchers in almost all disciplines. Statistical distribution as a mathematical function that explain the relationship between observations of different heights. The distribution provides a parameterized mathematical function that can be used to calculate the probability for any

**individual observation**from the sample space.

## Types of Distributions

- Continuous probability distributions
- Discrete probability distributions

**probability distributions**are probabilities associated with random variables that are able to assume any of an

**infinite number of values**, and therefore uncountable. For example, time is infinite: you could count from 0 seconds to infinite.

- Normal Distribution
- Exponential Distribution
- Chi-Square Distribution
- Uniform Distribution

**probability distributions**are listings of all possible outcomes of an experiment, this means that range of values that are

**countable**.

- Bernoulli Distribution
- Binomial Distribution
- Poisson Distribution
- Geometric Distribution

## Normal Distribution

The**Normal Distribution**, also known as the Gaussian distribution, is a continuous probability distribution that fits the

**probability distribution**of many events, eg. IQ Scores, Heartbeat etc. It is symmetrical on both sides of the mean, so the right side of the center is a mirror image of the left side. Normal distributions are symmetrical, but not all

**symmetrical distributions**are normal. It is often called a "Bell Curve" because it looks like a bell.

## Exponential Distribution

The**exponential distribution**is a continuous probability distribution that is often concerned with the amount of time until some specific event occurs (time elapsed between events). For example, How long do you need to wait until a customer enters a shop? Sometimes it is also called

**negative exponential distribution**. This type of distribution is mostly used in the field of reliability. Reliability deals with the amount of time a product lasts.

## Chi-Square Distribution

A**Chi-Square Distribution**is a continuous distribution that is used to describe the distribution of a sum of squared random variables. The degrees of freedom of the distribution is equal to the number of standard normal deviates being summed. Two common tests that rely on the

**Chi-square distribution**are:

- Chi-square goodness of fit test
- Chi-square test of independence

## Uniform Distribution

The**Uniform Distribution**, also known as the Rectangular Distribution, is a type of Continuous

**Probability Distribution**where every possible outcome has an equal likelihood of happening. The probability is constant since each variable has

**equal chances**of being the outcome. It is used in random number generating techniques such as the inversion method.

## Bernoulli Distribution

A**Bernoulli Distribution**is a discrete probability distribution that models random variables that have only two possible values. The two possible values of a

**Bernoulli random variable**are usually 0 and 1. An example is the outcome of a coin toss, where the outcome is either a head (success) or a tail (failure) and the probability of a head is a number between 0 and 1.

## Binomial Distribution

A**Binomial Distribution**, a common distribution function for discrete processes, is used when there are exactly two

**mutually exclusive**outcomes of a trial. For example the outcome of tossing a coin is head or tail, is usually refer to one outcome as "success" and the other outcome as "failure".

## Poisson Distribution

The**Poisson Distribution**is a discrete distribution that measures the probability of a given number of events happening in a

**specified time period**. This means that it measures how many times an event is likely to occur within 'x' period of time.

## Geometric Distribution

Geometric Distribution, a**discrete probability distribution**, deals with the number of trials required for a single success. This means that it gives the probability of achieving success after N number of failures. So, it is a

**negative binomial distribution**where the number of successes (r) is equal to 1.

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