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Bernoulli Distribution

The mean of a bernoulli distribution, also called the expected value, represents the long run average outcome of repeated independent trials.

Suchibrata Patra

August 2026  ·  12 min read

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Bar chart probability mass function of a Binomial distribution, showing the probability of each possible count of successes from 0 to n.
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Binomial Distribution

Binomial distribution is a probability distribution, widely used to model the number of successes in a fixed number of independent random trials, where each trial has only two possible outcomes: success or failure. This distribution is useful for calculating the probability of a specific number of successes in scenarios like flipping coins, quality control, or survey predictions.

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Decaying curve of an Exponential distribution probability density function, tallest at zero and falling off smoothly toward the right.
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Exponential Distribution

The Exponential Distribution is one of the most commonly used probability distributions in statistics and data science. It is widely used to model the time or space between events in a Poisson process. In simple terms, it describes how long you have to wait before something happens, like a bus arriving or a customer calling a help center. For example, if buses arrive at a bus stop every 15 minutes on average, the time you wait for the next bus can be modelled using an exponential distribution.

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Bar chart probability mass function of a Geometric distribution, showing the probability of the first success occurring on each trial.
Article · August 2026

Geometric Distribution

A geometric distribution is a discrete probability distribution that gives the probability that the first success occurs on a specific trial in a sequence of independent Bernoulli trials, where each trial has two outcomes, success or failure, and the probability of success, p, remains constant across trials.

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Bar chart probability mass function of a Hypergeometric distribution, showing the probability of each possible number of successes drawn without replacement from a finite population.
Article · August 2026

Hypergeometric Distribution

The hypergeometric distribution models the probability of obtaining a specific number of successes in a given number of draws from a finite population. Unlike the binomial distribution, which assumes replacement, the hypergeometric distribution does not replace items once they are drawn. This characteristic makes it applicable in scenarios where the population size is fixed, and the number of items is limited.

Suchibrata Patra

Bar chart probability mass function of a Negative Binomial distribution, showing the probability of each possible number of failures before the r-th success.
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Negative Binomial Distribution

The negative binomial distribution models the number of trials needed to achieve a specified number of successes in a sequence of independent and identically distributed Bernoulli trials.

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Bell-shaped curve of a Normal distribution centered at the mean, showing symmetric tapering on both sides.
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Normal Distribution

A complete, visual guide to the Normal (Gaussian) distribution: the bell curve formula, notation, mean and standard deviation, symmetry, skewness and kurtosis, the empirical rule, the standard normal table, worked examples, related distributions, and where it shows up in statistics and machine learning.

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Bar chart probability mass function of a Poisson distribution, showing the probability of each possible event count for a fixed rate lambda.
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Poisson Distribution

The Poisson distribution is a discrete probability distribution that calculates the likelihood of a certain number of events occurring within a fixed interval of time, assuming the events occur independently.

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Flat rectangular curve of a Uniform distribution over an interval, showing constant height between two endpoints and zero elsewhere.
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Uniform Distribution

A complete, visual guide to the Uniform distribution: the discrete and continuous forms, the flat-density formula, notation, mean and variance, the CDF, moments and the moment generating function, worked examples, related distributions, and where it shows up in statistics, simulation and machine learning.

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