{"id":155562,"date":"2022-03-26T00:47:03","date_gmt":"2022-03-25T19:17:03","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/probability-mass-function\/"},"modified":"2022-12-31T14:53:46","modified_gmt":"2022-12-31T09:23:46","slug":"probability-mass-function","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/probability-mass-function\/","title":{"rendered":"Probability Mass Function"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/probability-mass-function\/#Its_effortless_to_find_the_PMF_for_a_variable_Given_below_are_the_steps_that_you_need_to_follow_to_find_the_PMF_of_a_variable\" title=\"It\u2019s effortless to find the PMF for a variable. Given below are the steps that you need to follow to find the PMF of a variable:\">It\u2019s effortless to find the PMF for a variable. Given below are the steps that you need to follow to find the PMF of a variable:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/probability-mass-function\/#Probability_Mass_Function_Definition\" title=\"Probability Mass Function Definition\">Probability Mass Function Definition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/probability-mass-function\/#Probability_Mass_Function\" title=\" Probability Mass Function\"> Probability Mass Function<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/probability-mass-function\/#Finding_The_Probability_Mass_Function\" title=\"Finding The Probability Mass Function\">Finding The Probability Mass Function<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/probability-mass-function\/#Probability_Mass_Function_Applications\" title=\"Probability Mass Function Applications\">Probability Mass Function Applications<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/probability-mass-function\/#Probability_Mass_Function_Solved_Example\" title=\"Probability Mass Function Solved Example\">Probability Mass Function Solved Example<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Its_effortless_to_find_the_PMF_for_a_variable_Given_below_are_the_steps_that_you_need_to_follow_to_find_the_PMF_of_a_variable\"><\/span>It\u2019s effortless to find the PMF for a variable. Given below are the steps that you need to follow to find the PMF of a variable:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Step 1: Calculate the mean of the variable.<\/p>\n<p>Step 2: Calculate the standard deviation of the variable.<\/p>\n<p>Step 3: Divide the standard deviation by the square root of the number of observations.<\/p>\n<p>Step 4: Multiply the result by the probability of an event that is less than or equal to the value of the variable.<\/p>\n<p>Step 5: Add the result to 1.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-155561 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/probability-mass-function.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/probability-mass-function.jpg?v=1648235819 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/probability-mass-function-300x212.jpg?v=1648235819 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Probability_Mass_Function_Definition\"><\/span>Probability Mass Function Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A probability mass function (pmf) is a function that assigns a probability to each possible outcome of a random event. The function maps outcomes to real numbers in the range 0 to 1, with the sum of the probabilities for all outcomes equaling 1.<\/p>\n<p>For example, consider the roll of a fair six-sided die. The outcomes of the roll are 1, 2, 3, 4, 5, and 6, each of which has a probability of 1\/6. The pmf for this random event can be represented by the table below.<\/p>\n<p>Outcome Probability 1 1\/6 2 1\/6 3 1\/6 4 1\/6 5 1\/6 6 1\/6<\/p>\n<p>The pmf can also be represented by a graph, as shown below.<\/p>\n<h2> Probability Mass Function<\/h2>\n<p>The probability mass function (PMF) is a function that assigns a probability to each possible outcome of a random event. The PMF can be used to calculate the probability of a particular outcome occurring.<\/p>\n<p>The PMF for a random event can be represented by a histogram. The height of each bar in the histogram corresponds to the PMF for that outcome.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Finding_The_Probability_Mass_Function\"><\/span>Finding The Probability Mass Function<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The probability mass function (pmf) of a discrete random variable tells us how likely it is for the variable to take on a particular value. In other words, it tells us the probability of each value occurring.<\/p>\n<p>There are a few steps we need to take in order to find the pmf of a discrete random variable.<\/p>\n<p>1. First, we need to list all of the possible values the variable can take on.<\/p>\n<p>2. Next, we need to find the probability of each value occurring.<\/p>\n<p>3. Finally, we need to add up all of the probabilities to find the pmf.<\/p>\n<p>Let&#8217;s look at an example.<\/p>\n<p>Suppose we are interested in the probability of a die landing on a particular number.<\/p>\n<p>There are six possible values the die can land on, so we list them below:<\/p>\n<p>1 2 3 4 5 6<\/p>\n<p>We can find the probability of each value occurring by dividing the number of times the value appears on the die by the total number of rolls of the die.<\/p>\n<p>1 2 3 4 5 6 1\/6 1\/6 1\/6 1\/6 1\/6 1\/6<\/p>\n<p>We can add up all of the probabilities to find the pmf.<\/p>\n<p>1 2 3 4 5 6 1\/6 1\/6 1\/6 1\/6 1\/6 1\/6 1\/6 2\/36 3\/36 4\/36 5\/36 6<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Probability_Mass_Function_Applications\"><\/span>Probability Mass Function Applications<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A probability mass function (PMF) is a function that assigns a probability to each possible outcome of an event. In other words, it is a way of computing the probability of an event.<\/p>\n<p>There are many different applications for probability mass functions. Some of these applications include:<\/p>\n<p>1. Comparing the probabilities of different events<\/p>\n<p>2. Determining the odds of an event<\/p>\n<p>3. Calculating the expected value of a random variable<\/p>\n<p>4. Assessing the fairness of a game or gambling situation<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Probability_Mass_Function_Solved_Example\"><\/span>Probability Mass Function Solved Example<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The probability mass function of a random variable X is given by<\/p>\n<p>f(x) = {0.1, 0.2, 0.3, 0.4, 0.5}<\/p>\n<p>x<\/p>\n<p>{<\/p>\n<p>0.1<\/p>\n<p>,<\/p>\n<p>0.2<\/p>\n<p>,<\/p>\n<p>0.3<\/p>\n<p>,<\/p>\n<p>0.4<\/p>\n<p>,<\/p>\n<p>0.5<\/p>\n<p>}<\/p>\n<p>What is the probability that X is less than or equal to 0.2?<\/p>\n<p>The probability that X is less than or equal to 0.2 is 0.2.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>It\u2019s effortless to find the PMF for a variable. Given below are the steps that you need to follow to [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Probability Mass Function","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Probability Mass Function topic of Maths in details explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/probability-mass-function\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Probability Mass Function - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about Probability Mass Function topic of Maths in details explained by subject experts on infinitylearn.com.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/probability-mass-function\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Probability Mass Function - 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