{"id":11025,"date":"2024-05-28T15:58:12","date_gmt":"2024-05-28T15:58:12","guid":{"rendered":"https:\/\/milestone-institute.org\/modules\/probability\/"},"modified":"2026-07-24T15:15:05","modified_gmt":"2026-07-24T15:15:05","slug":"probability","status":"publish","type":"modules","link":"https:\/\/milestone-institute.org\/hu\/modules\/probability\/","title":{"rendered":"Probability"},"content":{"rendered":"<p><!-- MILESTONE MODULE PAGE \u2013 PROBABILITY --><\/p>\n<section aria-labelledby=\"module-title\"\n    style=\"width:calc(100% - 40px);\n           max-width:1180px;\n           margin:48px auto 72px;\n           box-sizing:border-box;\n           font-family:inherit;\n           color:#20252a;\"><\/p>\n<div style=\"overflow:hidden;\n                background:#f7f4ea;\n                border:1px solid #d8d2c4;\n                border-top:10px solid #f4c94f;\n                border-radius:0 0 18px 18px;\n                box-shadow:0 18px 48px rgba(25,29,32,0.09);\"><\/p>\n<p>        <!-- F\u0150 TARTALOM --><\/p>\n<div style=\"padding:clamp(26px,5vw,68px);\n                    box-sizing:border-box;\"><\/p>\n<p>            <!-- TUDOM\u00c1NYTER\u00dcLET --><\/p>\n<div style=\"display:flex;\n                        flex-wrap:wrap;\n                        gap:10px;\n                        margin:0 0 24px;\"><\/p>\n<p>                <span style=\"display:inline-block;\n                             padding:8px 14px;\n                             background:#f4c94f;\n                             border:1px solid #d3aa2e;\n                             border-radius:999px;\n                             font-size:13px;\n                             line-height:1;\n                             font-weight:700;\n                             letter-spacing:0.06em;\n                             text-transform:uppercase;\n                             color:#20252a;\"><br \/>\n                    Maths<br \/>\n                <\/span><\/p><\/div>\n<p>            <!-- MODULC\u00cdM --><\/p>\n<h1 id=\"module-title\"\n                lang=\"en\"\n                style=\"display:block;\n                       width:100%;\n                       max-width:100%;\n                       margin:0 0 22px;\n                       padding:0;\n                       box-sizing:border-box;\n                       font-size:clamp(30px,8vw,78px);\n                       line-height:1.02;\n                       letter-spacing:-0.035em;\n                       font-weight:700;\n                       color:#20252a;\n                       white-space:normal !important;\n                       overflow-wrap:anywhere;\n                       word-break:normal;\n                       hyphens:auto;\"><br \/>\n                Probability<br \/>\n            <\/h1>\n<p>            <!-- S\u00c1RGA ELV\u00c1LASZT\u00d3 --><\/p>\n<div aria-hidden=\"true\"\n                style=\"width:76px;\n                       height:4px;\n                       margin:0 0 30px;\n                       background:#f4c94f;\n                       border-radius:999px;\">\n            <\/div>\n<p>            <!-- MODULLE\u00cdR\u00c1S --><\/p>\n<div style=\"max-width:980px;\n                        margin:0;\n                        font-size:clamp(18px,1.55vw,24px);\n                        line-height:1.62;\n                        font-weight:400;\n                        color:#282d31;\"><\/p>\n<p style=\"margin:0;\">\n                    The module covers major topics in probability theory and statistics. We will introduce theoretical concepts through simple experiments and games. We will then discuss some important probability distributions: what kind of distribution should we use for lifetimes and waiting times, or for the number of mistypings on the pages of a newspaper? How can we describe a probability distribution through distribution functions, density functions and characteristic functions? We will explore the law of large numbers in mathematical form and the central limit theorem, including why the Gaussian, or Normal, distribution is special. These concepts are also used in financial mathematics. Together, they form the basis of statistics, providing tools for interpreting the world around us through estimates and hypothesis testing. These methods are used in the social sciences and medicine as well. The module is highly recommended for students wishing to study Mathematics, Economics or other numerical sciences at university, while students interested in certain fields of the natural sciences are also welcome.\n                <\/p>\n<\/p><\/div>\n<\/p><\/div>\n<p>        <!-- MODULVEZET\u0150 --><\/p>\n<div style=\"display:flex;\n                    flex-wrap:wrap;\n                    background:#f4c94f;\n                    border-top:1px solid #d3aa2e;\"><\/p>\n<div style=\"flex:1 1 260px;\n                        padding:26px clamp(28px,4vw,52px);\n                        box-sizing:border-box;\"><\/p>\n<div style=\"margin:0 0 9px;\n                            font-size:12px;\n                            line-height:1.2;\n                            font-weight:800;\n                            letter-spacing:0.1em;\n                            text-transform:uppercase;\n                            color:#20252a;\"><br \/>\n                    Module leader\n                <\/div>\n<div style=\"max-width:980px;\n                            font-size:clamp(17px,1.3vw,21px);\n                            line-height:1.55;\n                            font-weight:600;\n                            color:#20252a;\"><br \/>\n                    Mavroyiannis Diomedes\n                <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<p>        <!-- VISSZAL\u00c9P\u00c9S --><\/p>\n<div style=\"padding:22px clamp(28px,4vw,52px);\n                    background:#fffdf7;\n                    border-top:1px solid #d8d2c4;\"><\/p>\n<p>            <a href=\"https:\/\/milestone-institute.org\/modulkatalogus\/\"\n               style=\"display:inline-block;\n                      color:#20252a;\n                      font-size:16px;\n                      line-height:1.4;\n                      font-weight:700;\n                      text-decoration:none;\n                      border-bottom:2px solid #f4c94f;\n                      padding-bottom:3px;\"><br \/>\n                \u2190 Vissza a modulkatal\u00f3gushoz<br \/>\n            <\/a><\/p><\/div>\n<\/p><\/div>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>The module covers major topics of probability theory and statistics. We will introduce theoretical concepts through simple experiments and games. Then we discuss some important probability distributions: what kind of distribution we should use for lifetimes\/waiting times, or for the number of mistyping in the pages of a newspaper, etc. How can we describe a probability distribution: distribution, density functions (and also characteristic functions)? Law of large numbers in a mathematical formulation. Central limit theorem &#8211; or why the Gaussian (Normal) distribution is special. These concepts are used in financial mathematics. The above concepts form the basis of statistics: giving tools for appraising the world around us. Estimates, hypothesis testing. These are used in social sciences and medicine as well. The module is highly recommended for those wishing to study Mathematics, Economics, or other numerical sciences at university, but students interested in some fields of natural sciences are also welcome.<\/p>\n","protected":false},"featured_media":0,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"department":[],"division":[104],"terms_years":[252],"level":[247],"class_list":["post-11025","modules","type-modules","status-publish","format-standard","hentry","division-numerical-sciences","terms_years-2024-2025","level-immersion-2"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Probability &#8211; Milestone Institute<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/milestone-institute.org\/modules\/probability\/\" \/>\n<meta property=\"og:locale\" content=\"hu_HU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Probability &#8211; Milestone Institute\" \/>\n<meta property=\"og:description\" content=\"The module covers major topics of probability theory and statistics. We will introduce theoretical concepts through simple experiments and games. Then we discuss some important probability distributions: what kind of distribution we should use for lifetimes\/waiting times, or for the number of mistyping in the pages of a newspaper, etc. How can we describe a probability distribution: distribution, density functions (and also characteristic functions)? Law of large numbers in a mathematical formulation. Central limit theorem - or why the Gaussian (Normal) distribution is special. These concepts are used in financial mathematics. The above concepts form the basis of statistics: giving tools for appraising the world around us. Estimates, hypothesis testing. These are used in social sciences and medicine as well. The module is highly recommended for those wishing to study Mathematics, Economics, or other numerical sciences at university, but students interested in some fields of natural sciences are also welcome.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/milestone-institute.org\/modules\/probability\/\" \/>\n<meta property=\"og:site_name\" content=\"Milestone Institute\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/msinst\" \/>\n<meta property=\"article:modified_time\" content=\"2026-07-24T15:15:05+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Becs\u00fclt olvas\u00e1si id\u0151\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 perc\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/milestone-institute.org\\\/modules\\\/probability\\\/\",\"url\":\"https:\\\/\\\/milestone-institute.org\\\/modules\\\/probability\\\/\",\"name\":\"Probability &#8211; Milestone Institute\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/milestone-institute.org\\\/hu\\\/#website\"},\"datePublished\":\"2024-05-28T15:58:12+00:00\",\"dateModified\":\"2026-07-24T15:15:05+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/milestone-institute.org\\\/modules\\\/probability\\\/#breadcrumb\"},\"inLanguage\":\"hu\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/milestone-institute.org\\\/modules\\\/probability\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/milestone-institute.org\\\/modules\\\/probability\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Kezd\u0151lap\",\"item\":\"https:\\\/\\\/milestone-institute.org\\\/hu\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Probability\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/milestone-institute.org\\\/hu\\\/#website\",\"url\":\"https:\\\/\\\/milestone-institute.org\\\/hu\\\/\",\"name\":\"Milestone Institute\",\"description\":\"Milestone Institute\",\"publisher\":{\"@id\":\"https:\\\/\\\/milestone-institute.org\\\/hu\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/milestone-institute.org\\\/hu\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"hu\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/milestone-institute.org\\\/hu\\\/#organization\",\"name\":\"Milestone Institute\",\"url\":\"https:\\\/\\\/milestone-institute.org\\\/hu\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"hu\",\"@id\":\"https:\\\/\\\/milestone-institute.org\\\/hu\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/milestone-institute.org\\\/wp-content\\\/uploads\\\/2022\\\/10\\\/logo-mini.svg\",\"contentUrl\":\"https:\\\/\\\/milestone-institute.org\\\/wp-content\\\/uploads\\\/2022\\\/10\\\/logo-mini.svg\",\"width\":77,\"height\":85,\"caption\":\"Milestone Institute\"},\"image\":{\"@id\":\"https:\\\/\\\/milestone-institute.org\\\/hu\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/msinst\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Probability &#8211; Milestone Institute","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/milestone-institute.org\/modules\/probability\/","og_locale":"hu_HU","og_type":"article","og_title":"Probability &#8211; Milestone Institute","og_description":"The module covers major topics of probability theory and statistics. 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