{"id":6045,"date":"2023-03-28T19:00:00","date_gmt":"2023-03-28T19:00:00","guid":{"rendered":"https:\/\/modernsciences.org\/staging\/4414\/?p=6045"},"modified":"2023-03-29T06:10:09","modified_gmt":"2023-03-29T06:10:09","slug":"understanding-complex-population-phenomena-with-probability-models","status":"publish","type":"post","link":"https:\/\/modernsciences.org\/staging\/4414\/understanding-complex-population-phenomena-with-probability-models\/","title":{"rendered":"Understanding Complex Population Phenomena with Probability Models"},"content":{"rendered":"\n<p>A new approach to teaching statistics has been proposed based on phenomenology, a philosophy that seeks to understand human experience. Researchers have applied this method to teach fundamental statistics concepts such as random experiments, sample spaces, random variables, and probability distributions.<\/p>\n\n\n\n<p>The study begins by defining the terms used in statistical analysis. An experiment is defined as a replicable procedure that produces a visible result. Random experiments are those in which the result is not determined by the experimental conditions, but by the structure of the marks on a die, for example.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img  loading=\"lazy\"  decoding=\"async\"  width=\"1024\"  height=\"765\"  src=\"https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-pixabay-37534-80x60.jpg\"  alt=\"\"  class=\"wp-image-6049 pk-lqip pk-lazyload\"  data-pk-sizes=\"auto\"  data-ls-sizes=\"auto, (max-width: 1024px) 100vw, 1024px\"  data-pk-src=\"https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-pixabay-37534-1024x765.jpg\"  data-pk-srcset=\"https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-pixabay-37534-1024x765.jpg 1024w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-pixabay-37534-300x225.jpg 300w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-pixabay-37534-768x574.jpg 768w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-pixabay-37534-1536x1148.jpg 1536w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-pixabay-37534-200x150.jpg 200w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-pixabay-37534-260x195.jpg 260w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-pixabay-37534-380x284.jpg 380w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-pixabay-37534-800x598.jpg 800w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-pixabay-37534-1160x867.jpg 1160w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-pixabay-37534-80x60.jpg 80w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-pixabay-37534-400x300.jpg 400w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-pixabay-37534-760x568.jpg 760w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-pixabay-37534-1600x1196.jpg 1600w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-pixabay-37534-600x448.jpg 600w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-pixabay-37534.jpg 1920w\" ><figcaption class=\"wp-element-caption\">(<a href=\"https:\/\/www.pexels.com\/@pixabay\/\" target=\"_blank\" rel=\"noopener\" title=\"Pixabay\">Pixabay<\/a>\/<a href=\"https:\/\/www.pexels.com\/\" target=\"_blank\" rel=\"noopener\" title=\"Pexels\">Pexels<\/a>, 2016)<\/figcaption><\/figure>\n\n\n\n<p>The study goes on to explore the population of observations of the results of a random experiment and the assumption of independence of the realizations of a random experiment. The assumption of independence is based on the idea that no other type of causality is involved in the experiment and that the repetition of the experiment produces independent results.<\/p>\n\n\n\n<p>The researchers also discuss Laplace\u2019s Rule, which is a method of assigning probabilities to the results of a random experiment. The sample space of a random experiment is defined as the set of all possible simple results. The study then introduces the concept of a random variable, which represents a random number present through an experiment.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img  loading=\"lazy\"  decoding=\"async\"  width=\"1024\"  height=\"683\"  src=\"https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-mike-chai-842339-80x53.jpg\"  alt=\"\"  class=\"wp-image-6048 pk-lqip pk-lazyload\"  data-pk-sizes=\"auto\"  data-ls-sizes=\"auto, (max-width: 1024px) 100vw, 1024px\"  data-pk-src=\"https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-mike-chai-842339-1024x683.jpg\"  data-pk-srcset=\"https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-mike-chai-842339-1024x683.jpg 1024w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-mike-chai-842339-1536x1025.jpg 1536w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-mike-chai-842339-380x254.jpg 380w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-mike-chai-842339-800x534.jpg 800w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-mike-chai-842339-1160x774.jpg 1160w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-mike-chai-842339-80x53.jpg 80w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-mike-chai-842339-760x507.jpg 760w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-mike-chai-842339-1600x1068.jpg 1600w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-mike-chai-842339-600x400.jpg 600w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-mike-chai-842339-300x200.jpg 300w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-mike-chai-842339-768x512.jpg 768w, https:\/\/modernsciences.org\/staging\/4414\/wp-content\/uploads\/2023\/03\/pexels-mike-chai-842339.jpg 1920w\" ><figcaption class=\"wp-element-caption\">(<a href=\"https:\/\/www.pexels.com\/@mike-chai-285623\/\" target=\"_blank\" rel=\"noopener\" title=\"Chai\">Chai<\/a>\/<a href=\"https:\/\/www.pexels.com\/\" target=\"_blank\" rel=\"noopener\" title=\"Pexels\">Pexels<\/a>, 2018)<\/figcaption><\/figure>\n\n\n\n<p>The researchers argue that the phenomenological approach is more intuitive and easier to understand than traditional statistical methods. Using everyday language and examples, they hope to make statistics more accessible to students. They also suggest that using subscripts and other mathematical symbols may hinder students\u2019 understanding of statistics.<\/p>\n\n\n\n<p>The study has implications for the teaching and learning of statistics in schools and universities. Educators can use the phenomenological approach to make statistics more engaging and relevant to students\u2019 lives. The researchers suggest that further research is needed to determine the effectiveness of this approach, but they believe that it has the potential to transform the way statistics is taught and learned.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><br>Link to the article: <a href=\"https:\/\/journals.modernsciences.org\/index.php\/msj\/article\/view\/21\" target=\"_blank\" rel=\"noopener\" title=\"\">https:\/\/journals.modernsciences.org\/index.php\/msj\/article\/view\/21<\/a><\/p>\n<cite>Summary of: <strong>The Idea of a Probability Model for a Population<\/strong>, by H\u00e9ctor Hevia<\/cite><\/blockquote>\n\n\n\n<h1 id=\"references\" class=\"wp-block-heading\">References<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Hevia, H. (2023). The Idea of a Probability Model for a Population. <em>Modern Sciences Journal<\/em>, <em>12<\/em>(1). <a href=\"https:\/\/doi.org\/10.57184\/msj.v12i1.21\" target=\"_blank\" rel=\"noopener\" title=\"\">https:\/\/doi.org\/10.57184\/msj.v12i1.21<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"A new approach to teaching statistics has been proposed based on phenomenology, a philosophy that seeks to understand&hellip;\n","protected":false},"author":4,"featured_media":5994,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","fifu_image_url":"","fifu_image_alt":"","footnotes":""},"categories":[17,735,742],"tags":[129,721,710],"class_list":{"0":"post-6045","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-math-and-the-sciences","8":"category-modern-sciences-journal","9":"category-vol-12-no-1-2023","10":"tag-mathematics","11":"tag-modern-sciences-journal","12":"tag-probability","13":"cs-entry","14":"cs-video-wrap"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/posts\/6045","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/comments?post=6045"}],"version-history":[{"count":1,"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/posts\/6045\/revisions"}],"predecessor-version":[{"id":6050,"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/posts\/6045\/revisions\/6050"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/media\/5994"}],"wp:attachment":[{"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/media?parent=6045"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/categories?post=6045"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/modernsciences.org\/staging\/4414\/wp-json\/wp\/v2\/tags?post=6045"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}