{"id":3750,"date":"2021-07-12T21:13:46","date_gmt":"2021-07-12T15:43:46","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=3750"},"modified":"2021-10-30T07:40:34","modified_gmt":"2021-10-30T07:40:34","slug":"what-are-probability-distributions","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-are-probability-distributions\/","title":{"rendered":"What are probability distributions?"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\"><strong>Overview<\/strong>&#8211; probability distributions<\/h2>\n\n\n\n<p>The concept of probability and probability distributions is used when we are uncertain about future events.<\/p>\n\n\n\n<p>The study of probability distributions is an important parts of statistics.<\/p>\n\n\n\n<p>Probability theory is widely used in finance, healthcare, weather forecast, insurance, sports, etc. <\/p>\n\n\n\n<p>The concept of probability distribution gives the idea about the probabilities of any random experiment.<\/p>\n\n\n\n<p>The probability distribution indicates the likelihood of an outcome,<\/p>\n\n\n\n<p>Nowadays, stats and the concept of probability and its distributions has become a very important part of fields like data science, machine learning, artificial intelligence, computer science etc.<\/p>\n\n\n\n<figure class=\"wp-block-embed-youtube wp-block-embed is-type-video is-provider-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Probability: Types of Distributions\" width=\"1170\" height=\"658\" src=\"https:\/\/www.youtube.com\/embed\/b9a27XN_6tg?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Statistics &amp; probability<\/strong><\/h2>\n\n\n\n<p>Stats deals with the collection, organizing, analysing, interpreting, and presentation of the data.<\/p>\n\n\n\n<p>Mainly the statistics is divided into two parts-<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/KYkWccE8Lj20BbyUEoRoXBVqS_M-946p40I15P128hlO_rzSr70uuPxEUmkzC-vtuHHQJ9R9sVwYupVz3CpNuYhXQH_d4bAhN5-X1GpJTSBXcLpC7cEVqf9ZqF8lyLhdY1w10clA\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>Descriptive statistics deals with the properties of sample and population and inferential statistics deals, how to take decisions from the data (sample) by using various parameters.<\/p>\n\n\n\n<p>Topics we study in descriptive statistics are- mean, median, mode, SD, variance, skewness, kurtosis etc.<\/p>\n\n\n\n<p>In inferential statistics we study- regression analysis, analysis of variance(ANOVA), testing of hypotheses etc.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Probability<\/strong><\/h2>\n\n\n\n<p>We can not predict in many cases what will happen in the future. <\/p>\n\n\n\n<p>For example suppose we toss a coin, we do not know what will be the outcome, whether it is head or tail.<\/p>\n\n\n\n<p>If we throw a dice, we can not predict which number will come.<\/p>\n\n\n\n<p>In these cases, we use the idea of probability.<\/p>\n\n\n\n<p>The concept of probability is all about the possibilities.&nbsp;<\/p>\n\n\n\n<p>It predicts how likely events are to happen. Probability measures the likelihood of an event to occur.<\/p>\n\n\n\n<p>The value of probability always lies between 0 to 1.<\/p>\n\n\n\n<p>If the outcome is impossible then probability is zero, and if the outcome is certain the it is 1.<\/p>\n\n\n\n<p><strong>Random Experiment<\/strong><\/p>\n\n\n\n<p>An experiment in which we know all the possible outcomes but we can not say that or we can not predict which of them will occur when we perform the experiment.<\/p>\n\n\n\n<p><strong>Definition of probability (Classical)<\/strong><\/p>\n\n\n\n<p>&nbsp;Suppose there are \u2018n\u2019 exhaustive cases in a random experiment which is equally likely and mutually exclusive.<\/p>\n\n\n\n<p>Let \u2018m\u2019 cases are favourable for the happening of an event A, then the probability of happening event A can be defined as-<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/65m3kRixlBDEk35FSEuyfvRhVZefmkJ56I2wqzXee85iDI2k2AvtInzf052VJCYDsjpxNpozcsam6YlYnM5cXd0Zl7Uaj0qW9PhtAosNefSUm2Z32ePslhHBN0R6xfVDK_ksDNAP\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>Probability of non-happening of the event A is defined as-<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/s7CV6xc6l3l7wpk2pKqcJP5wkqg6CMxL5Fkl4zhdx2X9zRu8WRZHX9JKLbZCh2Sfb9-jdb4a3fuSa2Yo_2l7x0HQn9-t_LtF9nOo52vN8C4FPvDDL9Krpf-tKOxxa9szvOMGPgyJ\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>The classical definition of probability fails if-<\/p>\n\n\n\n<p>1. &nbsp; &nbsp; The cases are not equally likely.<\/p>\n\n\n\n<p>2. &nbsp; &nbsp; The number of exhaustive cases are indefinitely large.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Probability distributions<\/strong><\/h2>\n\n\n\n<p>We can write a probability distribution in the form of an equation or a table.<\/p>\n\n\n\n<p>We can calculate the probability distribution from simple events to complex events.<\/p>\n\n\n\n<p>Suppose a coin is tossed, then its probability distribution can be tabulated as below-<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Number of heads<\/td><td>Probability<\/td><\/tr><tr><td>0<\/td><td>0.25<\/td><\/tr><tr><td>1<\/td><td>0.50<\/td><\/tr><tr><td>2<\/td><td>0.25<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Note- Sum of all the probabilities is always 1.<\/p>\n\n\n\n<p>There are two important terms we use in probability distribution- expected value and variance.<\/p>\n\n\n\n<p>Expected value is the average value of a random variable and variance is the average spread of values around expected values.<\/p>\n\n\n\n<p>There are two type of probability distribution-<\/p>\n\n\n\n<p>1. &nbsp; &nbsp; Discrete probability distributions<\/p>\n\n\n\n<p>2. &nbsp; &nbsp; Continuous probability distributions.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/IH_jcc1v-Mv6ejARmutzqkvaICrgRHkAsBGEk0mxcfNtNOJXlukOx3pzkpPah0tEugofdVHZFBzNV-SnsecgsSZtlSNBRZlXbk-0Al5-AmEivx0PO92CfFRKRg3WXeYpj-JO8l8U\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>If the random variable is discrete, then it will have a discrete probability distribution.<\/p>\n\n\n\n<p>Discrete probability distributions(Example)-<\/p>\n\n\n\n<p>Suppose we throw a dice then the probabilities associated with the outcomes form a discrete uniform distribution.<\/p>\n\n\n\n<p>The probabilities of tossing a coin from a Bernoulli distribution<\/p>\n\n\n\n<p>The probabilities of the cars passing through a road within a fixed period from a Poisson distribution.<\/p>\n\n\n\n<p>Discrete probability distributions are-<\/p>\n\n\n\n<p>1. &nbsp; &nbsp; Binomial distribution<\/p>\n\n\n\n<p>2. &nbsp; &nbsp; Bernoulli distribution<\/p>\n\n\n\n<p>3. &nbsp; &nbsp; Geometric distribution<\/p>\n\n\n\n<p>4. &nbsp; &nbsp; Hyper-geometric distribution<\/p>\n\n\n\n<p>5. &nbsp; &nbsp; Multinomial distribution<\/p>\n\n\n\n<p>6. &nbsp; &nbsp; Poisson distribution<\/p>\n\n\n\n<p>7. &nbsp; &nbsp; Negative binomial distribution<\/p>\n\n\n\n<p>Continuous probability distributions are-<\/p>\n\n\n\n<p>1. &nbsp; &nbsp; Normal distribution<\/p>\n\n\n\n<p>2. &nbsp; &nbsp; Pareto distribution<\/p>\n\n\n\n<p>3. &nbsp; &nbsp; Beta distribution<\/p>\n\n\n\n<p>4. &nbsp; &nbsp; Cauchy distribution<\/p>\n\n\n\n<p>5. &nbsp; &nbsp; Gamma distribution<\/p>\n\n\n\n<p>6. &nbsp; &nbsp; Logistic distribution<\/p>\n\n\n\n<p>7. &nbsp; &nbsp; Weibull distribution<\/p>\n\n\n\n<p>Interested in learning about similar topics? Here are a few hand-picked blogs for you!<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"https:\/\/www.goseeko.com\/blog\/__trashed-4\" target=\"_blank\" rel=\"noreferrer noopener\">What is normal distribution?<\/a><\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>The concept of probability distributions gives the idea about the probabilities of any random experiment. let&#8217;s know more about probability distributions.<\/p>\n","protected":false},"author":3,"featured_media":2992,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[31],"tags":[],"class_list":["post-3750","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.3.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What are probability 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