{"id":290,"date":"2017-04-15T03:20:47","date_gmt":"2017-04-15T03:20:47","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/conceptstest1\/chapter\/wrap-up-probability-and-probability-distributions\/"},"modified":"2019-09-30T05:40:08","modified_gmt":"2019-09-30T05:40:08","slug":"introduction-continuous-probability-distribution","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/chapter\/introduction-continuous-probability-distribution\/","title":{"raw":"Introduction to Continuous Probability Distribution","rendered":"Introduction to Continuous Probability Distribution"},"content":{"raw":"<h2>What you'll learn to do: Use a probability distribution for a continuous random variable to estimate probabilities and identify unusual events.<\/h2>\r\n<img class=\"alignright wp-image-2033\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1768\/2017\/04\/28155626\/Histogram-estim-pdf.png\" alt=\"A sample histogram with a line that estimates data.\" width=\"400\" height=\"258\" \/>\r\n\r\nIn the last section, we studied discrete (listable) random variables and their distributions. Now we explore continuous (decimal valued) random variables that can take on values anywhere in an interval. For example, a person\u2019s exact weight without rounding is a continuous random variable. If rounded to the nearest pound, weight is a discrete random variable. Decimal valued numbers arise often in real life, often in measuring things such as weight or length. To best study real life data that has values lying all over an interval, we need to build a solid foundation in continuous probability distributions.\r\n<h2>Contribute!<\/h2><div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div><a href=\"https:\/\/docs.google.com\/document\/d\/19xsJ0BrVampSfKmn358LWAek-bFGRzjknl3B2BZBAzs\" target=\"_blank\" style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\">Improve this page<\/a><a style=\"margin-left: 16px;\" target=\"_blank\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\">Learn More<\/a>","rendered":"<h2>What you&#8217;ll learn to do: Use a probability distribution for a continuous random variable to estimate probabilities and identify unusual events.<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignright wp-image-2033\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1768\/2017\/04\/28155626\/Histogram-estim-pdf.png\" alt=\"A sample histogram with a line that estimates data.\" width=\"400\" height=\"258\" \/><\/p>\n<p>In the last section, we studied discrete (listable) random variables and their distributions. Now we explore continuous (decimal valued) random variables that can take on values anywhere in an interval. For example, a person\u2019s exact weight without rounding is a continuous random variable. If rounded to the nearest pound, weight is a discrete random variable. Decimal valued numbers arise often in real life, often in measuring things such as weight or length. To best study real life data that has values lying all over an interval, we need to build a solid foundation in continuous probability distributions.<\/p>\n<h2>Contribute!<\/h2>\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div>\n<p><a href=\"https:\/\/docs.google.com\/document\/d\/19xsJ0BrVampSfKmn358LWAek-bFGRzjknl3B2BZBAzs\" target=\"_blank\" style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\">Improve this page<\/a><a style=\"margin-left: 16px;\" target=\"_blank\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\">Learn More<\/a><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-290\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Concepts in Statistics. <strong>Provided by<\/strong>: Open Learning Initiative. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/oli.cmu.edu\">http:\/\/oli.cmu.edu<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":163,"menu_order":15,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Concepts in Statistics\",\"author\":\"\",\"organization\":\"Open Learning Initiative\",\"url\":\"http:\/\/oli.cmu.edu\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"1ea85a9c-4dc3-4cbc-bba0-ed1850a1414e","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-290","chapter","type-chapter","status-publish","hentry"],"part":258,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/290","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/users\/163"}],"version-history":[{"count":14,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/290\/revisions"}],"predecessor-version":[{"id":2040,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/290\/revisions\/2040"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/parts\/258"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapters\/290\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/media?parent=290"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/pressbooks\/v2\/chapter-type?post=290"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/contributor?post=290"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-concepts-statistics\/wp-json\/wp\/v2\/license?post=290"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}