{"id":1024,"date":"2023-06-22T01:45:08","date_gmt":"2023-06-22T01:45:08","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/probability-distributions-dig-deeper\/"},"modified":"2025-05-16T02:20:50","modified_gmt":"2025-05-16T02:20:50","slug":"probability-distributions-dig-deeper","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/probability-distributions-dig-deeper\/","title":{"raw":"Probability Distributions: Fresh Take","rendered":"Probability Distributions: Fresh Take"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Understand the concept of a probability distribution and its role in describing the behavior of a random variable.<\/li>\r\n\t<li>Describe the characteristics of probability distributions.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>When creating a probability distribution, we can estimate the probabilities empirically using a <strong>simulation<\/strong>.<\/p>\r\n<p>At a college baseball stadium, every game features a race between three mascots: one dressed as a peanut, one dressed as a hot dog, and one dressed as a cup of soda. The winner of the race determines what discount will be available at the concession stand for the rest of the game: [latex]$1[\/latex] bags of peanuts, [latex]$1[\/latex] hot dogs, or [latex]$1[\/latex] soft drinks. For now, let\u2019s assume that all three mascots are equally likely to win the race, and each race is independent.<\/p>\r\n<p>Since we\u2019re assuming all three mascots are equally likely to win in each race, let's say that our statistics class decides to carry out the simulation by rolling dice: 1 and 2 represent Peanut, 3 and 4 represent Hot Dog, and 5 and 6 represent Soda.\u00a0How many times would you expect to get discounted peanuts if you attended 10 games?<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1002[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1003[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1106[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Understand the concept of a probability distribution and its role in describing the behavior of a random variable.<\/li>\n<li>Describe the characteristics of probability distributions.<\/li>\n<\/ul>\n<\/section>\n<p>When creating a probability distribution, we can estimate the probabilities empirically using a <strong>simulation<\/strong>.<\/p>\n<p>At a college baseball stadium, every game features a race between three mascots: one dressed as a peanut, one dressed as a hot dog, and one dressed as a cup of soda. The winner of the race determines what discount will be available at the concession stand for the rest of the game: [latex]$1[\/latex] bags of peanuts, [latex]$1[\/latex] hot dogs, or [latex]$1[\/latex] soft drinks. For now, let\u2019s assume that all three mascots are equally likely to win the race, and each race is independent.<\/p>\n<p>Since we\u2019re assuming all three mascots are equally likely to win in each race, let&#8217;s say that our statistics class decides to carry out the simulation by rolling dice: 1 and 2 represent Peanut, 3 and 4 represent Hot Dog, and 5 and 6 represent Soda.\u00a0How many times would you expect to get discounted peanuts if you attended 10 games?<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1002\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1002&theme=lumen&iframe_resize_id=ohm1002&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1003\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1003&theme=lumen&iframe_resize_id=ohm1003&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1106\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1106&theme=lumen&iframe_resize_id=ohm1106&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":11,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":3053,"module-header":"fresh_take","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1024"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":11,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1024\/revisions"}],"predecessor-version":[{"id":5945,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1024\/revisions\/5945"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/3053"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1024\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1024"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1024"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1024"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1024"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}