{"id":250,"date":"2021-07-14T15:58:59","date_gmt":"2021-07-14T15:58:59","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/introduction-continuous-random-variables\/"},"modified":"2021-11-11T19:54:07","modified_gmt":"2021-11-11T19:54:07","slug":"why-it-matters-continuous-random-variables","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/why-it-matters-continuous-random-variables\/","title":{"raw":"Why It Matters: Continuous Random Variables","rendered":"Why It Matters: Continuous Random Variables"},"content":{"raw":"<h2>How are continuous random variables related to inference?<\/h2>\r\nIn the previous module, <em>Discrete Random Variables<\/em>, the focus was on random variables where the outcome was a countable number.\u00a0 For example, the number of people living in a household and the probabilities associated with the number of people living in a household would be an example of a discrete random variable.\r\n\r\nHowever, there are often variables that can take on any value within a range of values. These types of variables are called <strong>continuous random variables<\/strong>. New car prices, hours of sleep a person sleeps each night and weights of pumpkins would be examples of continuous random variables. Probabilities associated with the continuous random variable depend on the shape of the distribution.\r\n\r\nUnderstanding probability for continuous distributions gets us one step closer to making decisions about the population based on a sample.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15032014\/m6_probability_big_picture_probability.gif\" alt=\"The Big Picture of statistics. Shown on the diagram are Step 1: Producing Data, Step 2: Exploratory Data Analysis, Step 3: Probability, and Step 4: Inference. Highlighted in this diagram is Step 3: Probability\" width=\"868\" height=\"420\" \/>","rendered":"<h2>How are continuous random variables related to inference?<\/h2>\n<p>In the previous module, <em>Discrete Random Variables<\/em>, the focus was on random variables where the outcome was a countable number.\u00a0 For example, the number of people living in a household and the probabilities associated with the number of people living in a household would be an example of a discrete random variable.<\/p>\n<p>However, there are often variables that can take on any value within a range of values. These types of variables are called <strong>continuous random variables<\/strong>. New car prices, hours of sleep a person sleeps each night and weights of pumpkins would be examples of continuous random variables. Probabilities associated with the continuous random variable depend on the shape of the distribution.<\/p>\n<p>Understanding probability for continuous distributions gets us one step closer to making decisions about the population based on a sample.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1729\/2017\/04\/15032014\/m6_probability_big_picture_probability.gif\" alt=\"The Big Picture of statistics. Shown on the diagram are Step 1: Producing Data, Step 2: Exploratory Data Analysis, Step 3: Probability, and Step 4: Inference. Highlighted in this diagram is Step 3: Probability\" width=\"868\" height=\"420\" \/><\/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-250\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li><strong>Provided by<\/strong>: Lumen Learning. <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 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":169134,"menu_order":1,"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\":\"\"},{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-250","chapter","type-chapter","status-publish","hentry"],"part":249,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/250","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/250\/revisions"}],"predecessor-version":[{"id":2636,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/250\/revisions\/2636"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/249"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/250\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=250"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=250"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=250"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=250"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}