Binomial distribution

As explained in Starting Data Analytics with Generative AI and Python

A binomial distribution gives the probabilities of the number of successes in a fixed number of independent Bernoulli trials with a common success probability.

A binomial distribution models the number of successes across a fixed number of independent trials, where every trial has the same success probability. It applies to binary outcomes such as success/failure, yes/no, or 1/0. section 2.6.1

Ten trials

With n=10 trials, the distribution shows the probability of 0, 1, 2, and up to 10 successes. More than two bars therefore represent aggregate results across multiple binary trials, not more than two outcomes from one trial. section 2.6.1

Practical applications include:

• Conversion rates in A/B testing. section 2.6.1
• Pass/fail rates in quality control. section 2.6.1
• Click-through rates in online advertising. section 2.6.1

Figure 2.2 Commonly encountered data distributions

Compare the binomial distribution with other commonly encountered data distributions. section 2.6.1

How Starting Data Analytics with Generative AI and Python covers it

How deep it goes

Defines the distribution and clarifies its n+1 aggregate outcomes through a ten-trial example.

Examples

Uses coin flipping, A/B-test conversions, quality-control pass rates, advertising clicks, and ten-trial success counts.

What you can do after

Evaluate/understand whether binary-trial data represent individual outcomes or counts of successes across multiple trials.

How it connects

Connects binary outcomes with Bernoulli trials and contrasts the model with the normal distribution.

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Also explained in

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  Statistics Every Programmer NeedsA binomial distribution gives the probabilities of the number of successes in a fixed number of independent binary trials with a common success probability.
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  Math and Architectures of Deep LearningA discrete probability distribution giving the chance of exactly k successes in n independent trials with constant success probability π.
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  Grokking StatisticsA binomial distribution gives the probabilities of obtaining a specified number of successes in a fixed number of independent Bernoulli trials.
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  Machine Learning System DesignA probability distribution for the number of successes in a fixed number of independent Bernoulli trials with a common success probability.
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  Fabulous Adventures in Data Structures and AlgorithmsA binomial distribution gives the probabilities of obtaining each possible number of successes in a fixed number of independent trials with the same success probability.

Compare how 6 books explain binomial distribution →

Related concepts

• probability distributionkind of · A probability distribution is a mathematical specification assigning probabilities to the possible values or outcomes of a random variable, with total probability one.
• Bernoulli distributionequivalent to · A Bernoulli distribution is a discrete probability distribution for one binary outcome, assigning probability p to one outcome and 1−p to the other.
• rotational gateuses · A rotational gate is a single-qubit quantum gate that rotates a qubit’s state by a specified angle about the Y axis of the Bloch sphere.
• Poisson distributionequivalent to · The Poisson distribution is a discrete probability distribution that models the count of events occurring independently at a constant average rate within a fixed interval or exposure.
• multiplication ruleuses · The multiplication rule determines a combined count or probability by multiplying the numbers of choices or the relevant probabilities at successive stages.

This explainer was generated by Manning's knowledge graph from the text of Starting Data Analytics with Generative AI and Python. The section links point to the parts of the book it draws on.