{"id":530,"date":"2017-01-07T16:21:34","date_gmt":"2017-01-07T16:21:34","guid":{"rendered":"http:\/\/muthu.co\/?p=530"},"modified":"2021-05-24T03:51:44","modified_gmt":"2021-05-24T03:51:44","slug":"understanding-binomial-distribution-using-python","status":"publish","type":"post","link":"http:\/\/write.muthu.co\/understanding-binomial-distribution-using-python\/","title":{"rendered":"Understanding Binomial Distribution using Python"},"content":{"rendered":"\n<p>Binomial distribution is used to understand the probability of a particular outcome in repeated independent trials. The probability of a&nbsp;trial is either success or failure.&nbsp;The trials are independent as the outcome or the previous trial had no effect on the next trial, as happens in&nbsp;tossing of coins.<\/p>\n\n\n\n<p>If we flip a coin, it would either be HEADs or TAILs. Normal probability is 0.5 for both p(H) and p(T). In binomial terms we say p(H) is the probability of a HEAD showing up in a trial and 1-p(H) if head doesn&#8217;t show up.<\/p>\n\n\n\n<p>If the coin is flipped six times, then getting three heads has the maximum probability, whereas getting a single head or five heads has the least probability. This can be calculated using the below code in python.<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>from scipy.stats import binom\nimport matplotlib.pyplot as plt\n\nfig, ax = plt.subplots(1, 1)\nx = range(7)\nn, p = 6, 0.5\nrv = binom(n, p)\nax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1,label='Probablity of Success')          \nax.legend(loc='best', frameon=False)          \nplt.show()<\/code><\/pre>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"https:\/\/muthu.co\/wp-content\/uploads\/2017\/01\/figure_1-1-1.png\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"600\" src=\"https:\/\/muthu.co\/wp-content\/uploads\/2017\/01\/figure_1-1-1.png\" alt=\"\" class=\"wp-image-532\" srcset=\"http:\/\/write.muthu.co\/wp-content\/uploads\/2017\/01\/figure_1-1-1.png 800w, http:\/\/write.muthu.co\/wp-content\/uploads\/2017\/01\/figure_1-1-1-300x225.png 300w, http:\/\/write.muthu.co\/wp-content\/uploads\/2017\/01\/figure_1-1-1-768x576.png 768w, http:\/\/write.muthu.co\/wp-content\/uploads\/2017\/01\/figure_1-1-1-700x525.png 700w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><\/figure><\/div>\n\n\n\n<p>Another example:&nbsp;Suppose a die is tossed 5 times. What is the probability of getting exactly 2 fours?<\/p>\n\n\n\n<p>The probability of any outcome is 1\/6=0.167. Our code would look like<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>from scipy.stats import binom\nimport matplotlib.pyplot as plt\n\nfig, ax = plt.subplots(1, 1)\nx = range(6)\nn, p = 5, 0.166\nrv = binom(n, p)\nax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1,label='Probablity')          \nax.legend(loc='best', frameon=False)          \nplt.show()<\/code><\/pre>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"https:\/\/muthu.co\/wp-content\/uploads\/2017\/01\/figure_1-2.png\"><img loading=\"lazy\" decoding=\"async\" width=\"800\" height=\"600\" src=\"https:\/\/muthu.co\/wp-content\/uploads\/2017\/01\/figure_1-2.png\" alt=\"\" class=\"wp-image-533\" srcset=\"http:\/\/write.muthu.co\/wp-content\/uploads\/2017\/01\/figure_1-2.png 800w, http:\/\/write.muthu.co\/wp-content\/uploads\/2017\/01\/figure_1-2-300x225.png 300w, http:\/\/write.muthu.co\/wp-content\/uploads\/2017\/01\/figure_1-2-768x576.png 768w, http:\/\/write.muthu.co\/wp-content\/uploads\/2017\/01\/figure_1-2-700x525.png 700w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/a><\/figure><\/div>\n\n\n\n<p>As you can see in the graph above, the probability of second 4 showing up in a throw of a die is&nbsp;0.161.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Binomial distribution is used to understand the probability of a particular outcome in repeated independent trials. The probability of a&nbsp;trial is either success or failure.&nbsp;The trials are independent as the outcome or the previous trial had no effect on the next trial, as happens in&nbsp;tossing of coins. If we flip a coin, it would either [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,32,31],"tags":[54,58,62],"_links":{"self":[{"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/posts\/530"}],"collection":[{"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/comments?post=530"}],"version-history":[{"count":4,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/posts\/530\/revisions"}],"predecessor-version":[{"id":1906,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/posts\/530\/revisions\/1906"}],"wp:attachment":[{"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/media?parent=530"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/categories?post=530"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/write.muthu.co\/wp-json\/wp\/v2\/tags?post=530"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}