--- title: How Gaussian Distribution Maximizes Entropy — The Proof description: The normal distribution, also known as the Gaussian distribution, maximizes entropy given specific constraints on mean and variance. This mathematical proof... canonical: https://daily.dev/posts/how-gaussian-distribution-maximizes-entropy-the-proof-zl2ng48ml twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: How Gaussian Distribution Maximizes Entropy — The Proof | daily.dev og:description: The normal distribution, also known as the Gaussian distribution, maximizes entropy given specific constraints on mean and variance. This mathematical proof... og:url: https://daily.dev/posts/how-gaussian-distribution-maximizes-entropy-the-proof-zl2ng48ml og:image: https://api.daily.dev/og/posts/ZL2NG48mL.png og:image:alt: How Gaussian Distribution Maximizes Entropy — The Proof og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # How Gaussian Distribution Maximizes Entropy — The Proof **[Medium](https://daily.dev/sources/medium_js)** · 3 min read · 1 upvotes · 0 comments ## Summary The normal distribution, also known as the Gaussian distribution, maximizes entropy given specific constraints on mean and variance. This mathematical proof explores why the normal distribution is prevalent and powerful, and its connection to entropy and statistical inference. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: --- Tags: [#statistics](https://daily.dev/tags/statistics) [View this post on daily.dev](https://daily.dev/posts/how-gaussian-distribution-maximizes-entropy-the-proof-zl2ng48ml) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} {"@context":"https://schema.org","@type":"TechArticle","headline":"How Gaussian Distribution Maximizes Entropy — The Proof","url":"https://daily.dev/posts/how-gaussian-distribution-maximizes-entropy-the-proof-zl2ng48ml","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/how-gaussian-distribution-maximizes-entropy-the-proof-zl2ng48ml"},"datePublished":"2024-05-07T23:16:16.806Z","dateModified":"2024-05-09T08:43:33.910Z","description":"The normal distribution, also known as the Gaussian distribution, maximizes entropy given specific constraints on mean and variance. This mathematical proof...","image":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/0787de4aa85c820f16f32c7ec3104030?_a=AQAEuiZ","thumbnailUrl":"https://media.daily.dev/image/upload/f_auto,q_auto/v1/posts/0787de4aa85c820f16f32c7ec3104030?_a=AQAEuiZ","isAccessibleForFree":true,"articleSection":"Medium","inLanguage":"en","publisher":{"@type":"Organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180}},"author":{"@type":"Organization","name":"Medium","logo":"https://media.daily.dev/image/upload/t_logo,f_auto/v1/logos/medium","url":"https://daily.dev/sources/medium_js"},"commentCount":0,"discussionUrl":"https://daily.dev/posts/how-gaussian-distribution-maximizes-entropy-the-proof-zl2ng48ml","interactionStatistic":[{"@type":"InteractionCounter","interactionType":{"@type":"LikeAction"},"userInteractionCount":1},{"@type":"InteractionCounter","interactionType":{"@type":"CommentAction"},"userInteractionCount":0}],"keywords":"statistics","timeRequired":"PT3M"} {"@context":"https://schema.org","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://daily.dev"},{"@type":"ListItem","position":2,"name":"Medium","item":"https://daily.dev/sources/medium_js"},{"@type":"ListItem","position":3,"name":"How Gaussian Distribution Maximizes Entropy — The Proof"}]} ```