{"id":22339,"date":"2018-07-24T03:20:32","date_gmt":"2018-07-24T03:20:32","guid":{"rendered":"https:\/\/data-flair.training\/blogs\/?p=22339"},"modified":"2026-04-28T12:14:26","modified_gmt":"2026-04-28T06:44:26","slug":"python-probability-distributions","status":"publish","type":"post","link":"https:\/\/data-flair.training\/blogs\/python-probability-distributions\/","title":{"rendered":"Probability Distributions in Python &#8211; Normal, Binomial, Poisson, Bernoulli"},"content":{"rendered":"<div class='__iawmlf-post-loop-links' style='display:none;' data-iawmlf-post-links='[{&quot;id&quot;:149,&quot;href&quot;:&quot;https:\\\/\\\/www.python.org&quot;,&quot;archived_href&quot;:&quot;http:\\\/\\\/web-wp.archive.org\\\/web\\\/20251206090101\\\/https:\\\/\\\/www.python.org\\\/&quot;,&quot;redirect_href&quot;:&quot;&quot;,&quot;checks&quot;:[{&quot;date&quot;:&quot;2025-12-06 12:20:59&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2025-12-09 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03:08:37&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-05-21 06:27:39&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-05-24 07:06:36&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-05-27 07:30:50&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-05-30 08:47:47&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-06-02 09:37:18&quot;,&quot;http_code&quot;:206},{&quot;date&quot;:&quot;2026-06-05 09:43:29&quot;,&quot;http_code&quot;:206}],&quot;broken&quot;:false,&quot;last_checked&quot;:{&quot;date&quot;:&quot;2026-06-05 09:43:29&quot;,&quot;http_code&quot;:206},&quot;process&quot;:&quot;done&quot;}]'><\/div>\n<p>After studying<strong>\u00a0<a href=\"https:\/\/data-flair.training\/blogs\/python-descriptive-statistics\/\" target=\"_blank\" rel=\"noopener\">Python Descriptive Statistics<\/a><\/strong>, now we are going to explore 4 Major Python Probability Distributions: Normal, Binomial, Poisson, and Bernoulli\u00a0Distributions in Python. Moreover, we will learn how to implement these Python probability distributions with <a href=\"https:\/\/data-flair.training\/blogs\/python-tutorial-for-beginners\/\" target=\"_blank\" rel=\"noopener\"><strong>Python Programming<\/strong><\/a>.<\/p>\n<h3>What is Python Probability Distribution?<\/h3>\n<p>A probability distribution is a function under probability theory and statistics- one that gives us how probable different outcomes are in an experiment. It describes events in terms of their probabilities; this is out of all possible outcomes. Let&#8217;s take the probability distribution of a fair coin toss. Here, heads take a value of X=0.5, and tails get X=0.5 too.<\/p>\n<p>Two classes of such a distribution are discrete and continuous. The former is represented by a probability mass function and the latter by a probability density function.<\/p>\n<p><strong>Why is probability distribution important?<\/strong><\/p>\n<ul>\n<li>It helps in understanding how the data behaves.<\/li>\n<li>It is also used in statistics, like the p-value.<\/li>\n<li>It helps in making predictions easier and identifying outliers.<strong><a href=\"https:\/\/data-flair.training\/blogs\/python-namedtuple\/\" target=\"_blank\" rel=\"noopener\">Do you know about Python Namedtuple<\/a>?<\/strong><\/li>\n<\/ul>\n<h3>How to Implement Python Probability Distributions?<\/h3>\n<p>Let&#8217;s implement these types of Python Probability Distributions, let&#8217;s see them:<\/p>\n<h4>a. Normal Distribution in Python<\/h4>\n<p>Python normal distribution is a function that distributes random variables in a graph that is shaped as a symmetrical bell. It does so by arranging the probability distribution for each value. Let\u2019s use <a href=\"https:\/\/data-flair.training\/blogs\/python-numpy-tutorial\/\" target=\"_blank\" rel=\"noopener\"><strong>Python numpy<\/strong> <\/a>for this.<\/p>\n<pre class=\"EnlighterJSRAW\">&gt;&gt;&gt; import scipy.stats\r\n&gt;&gt;&gt; import numpy as np\r\n&gt;&gt;&gt; import matplotlib.pyplot as plt\r\n&gt;&gt;&gt; np.random.seed(1234)\r\n&gt;&gt;&gt; samples=np.random.lognormal(mean=1.,sigma=.4,size=10000)\r\n&gt;&gt;&gt; shape,loc,scale=scipy.stats.lognorm.fit(samples,floc=0)\r\n&gt;&gt;&gt; num_bins=50\r\n&gt;&gt;&gt; clr=\"#EFEFEF\"\r\n&gt;&gt;&gt; counts,edges,patches=plt.hist(samples,bins=num_bins,color=clr)\r\n&gt;&gt;&gt; centers=0.5*(edges[:-1]+edges[1:])\r\n&gt;&gt;&gt; cdf=scipy.stats.lognorm.cdf(edges,shape,loc=loc,scale=scale)\r\n&gt;&gt;&gt; prob=np.diff(cdf)\r\n&gt;&gt;&gt; plt.plot(centers,samples.size*prob,'k-',linewidth=2)<\/pre>\n<p><strong>[&lt;matplotlib.lines.Line2D object at 0x0359E890&gt;]<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\">&gt;&gt;&gt; plt.show()<\/pre>\n<div id=\"attachment_22349\" style=\"width: 588px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/normal.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-22349\" class=\"wp-image-22349 size-full\" src=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/normal.png\" alt=\"Python\u00a0Probability Distributions - Normal\" width=\"578\" height=\"413\" srcset=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/normal.png 578w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/normal-150x107.png 150w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/normal-300x214.png 300w\" sizes=\"auto, (max-width: 578px) 100vw, 578px\" \/><\/a><p id=\"caption-attachment-22349\" class=\"wp-caption-text\">Implement Python\u00a0Probability Distributions &#8211;\u00a0Normal Distribution in Python<\/p><\/div>\n<h4>b. Binomial Distribution in Python<\/h4>\n<p>Python binomial distribution tells us the probability of how often there will be a success in <i>n<\/i> independent experiments. Such experiments are yes-no questions. One example may be tossing a coin.<br \/>\n<strong><a href=\"https:\/\/data-flair.training\/blogs\/scipy-tutorial\/\" target=\"_blank\" rel=\"noopener\">Let&#8217;s explore SciPy Tutorial \u2013 Linear Algebra, Benefits, Special Functions<\/a><\/strong><\/p>\n<pre class=\"EnlighterJSRAW\">&gt;&gt;&gt; import seaborn\r\n&gt;&gt;&gt; from scipy.stats import binom\r\n&gt;&gt;&gt; data=binom.rvs(n=17,p=0.7,loc=0,size=1010)\r\n&gt;&gt;&gt; ax=seaborn.distplot(data,\r\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0kde=True,\r\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0color='pink',\r\n\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0hist_kws={\"linewidth\": 22,'alpha':0.77})\r\n&gt;&gt;&gt; ax.set(xlabel='Binomial',ylabel='Frequency')<\/pre>\n<p><strong>[Text(0,0.5,&#8217;Frequency&#8217;), Text(0.5,0,&#8217;Binomial&#8217;)]<\/strong><\/p>\n<pre class=\"EnlighterJSRAW\">&gt;&gt;&gt; plt.show()<\/pre>\n<div id=\"attachment_22350\" style=\"width: 584px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/binomial.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-22350\" class=\"wp-image-22350 size-full\" src=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/binomial.png\" alt=\"Python\u00a0Probability Distributions - Binomial\" width=\"574\" height=\"445\" srcset=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/binomial.png 574w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/binomial-150x116.png 150w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/binomial-300x233.png 300w\" sizes=\"auto, (max-width: 574px) 100vw, 574px\" \/><\/a><p id=\"caption-attachment-22350\" class=\"wp-caption-text\">Implement Python\u00a0Probability Distributions &#8211; Binomial Distribution in Python<\/p><\/div>\n<h4 class=\"western\">c. Poisson Distribution in Python<\/h4>\n<p>Python Poisson distribution tells us about how probable it is that a certain number of events happen in a fixed interval of time or space. This assumes that these events happen at a constant rate and are also independent of the last event.<\/p>\n<pre class=\"EnlighterJSRAW\">&gt;&gt;&gt; import numpy as np\r\n&gt;&gt;&gt; s=np.random.poisson(5, 10000)\r\n&gt;&gt;&gt; import matplotlib.pyplot as plt\r\n&gt;&gt;&gt; plt.hist(s,16,normed=True,color='Green')<\/pre>\n<p>(array([5.86666667e-03, 3.55200000e-02, 8.86400000e-02, 1.48906667e-01,<br \/>\n1.91573333e-01, 1.81440000e-01, 1.56160000e-01, 1.16586667e-01,<br \/>\n6.65600000e-02, 3.90400000e-02, 2.06933333e-02, 9.06666667e-03,<br \/>\n3.84000000e-03, 2.13333333e-03, 5.33333333e-04, 1.06666667e-04]), array([ 0. , 0.9375, 1.875 , 2.8125, 3.75 , 4.6875, 5.625 ,<br \/>\n6.5625, 7.5 , 8.4375, 9.375 , 10.3125, 11.25 , 12.1875,<br \/>\n13.125 , 14.0625, 15. ]), &lt;a list of 16 Patch objects&gt;)<br \/>\n<a href=\"https:\/\/data-flair.training\/blogs\/python-interpreter\/\" target=\"_blank\" rel=\"noopener\"><strong>Read about What is Python Interpreter \u2013 Environment, Invoking &amp; Working<\/strong> <\/a><\/p>\n<pre class=\"EnlighterJSRAW\">&gt;&gt;&gt; plt.show()<\/pre>\n<div id=\"attachment_22351\" style=\"width: 591px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/poisson.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-22351\" class=\"wp-image-22351 size-full\" src=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/poisson.png\" alt=\"Python\u00a0Probability Distributions - poisson\" width=\"581\" height=\"422\" srcset=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/poisson.png 581w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/poisson-150x109.png 150w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/poisson-300x218.png 300w\" sizes=\"auto, (max-width: 581px) 100vw, 581px\" \/><\/a><p id=\"caption-attachment-22351\" class=\"wp-caption-text\">Implement Python\u00a0Probability Distributions &#8211; Poisson Distribution in Python<\/p><\/div>\n<h4 class=\"western\">d. Bernoulli Distribution in Python<\/h4>\n<p>Python\u00a0 Bernoulli Distribution is a case of binomial distribution where we conduct a single experiment. This is a discrete probability distribution with probability <i>p<\/i> for value 1 and probability <i>q=1-p<\/i> for value 0. <i>p<\/i> can be for success, yes, true, or one. Similarly, <i>q=1-p<\/i> can be for failure, no, false, or zero.<\/p>\n<pre class=\"EnlighterJSRAW\">&gt;&gt;&gt; s=np.random.binomial(10,0.5,1000)\r\n&gt;&gt;&gt; plt.hist(s,16,normed=True,color='Brown')<\/pre>\n<p>(array([0.00177778, 0.02311111, 0. , 0.08711111, 0. ,<br \/>\n0.18666667, 0. , 0.33777778, 0.45155556, 0. ,<br \/>\n0.37688889, 0. , 0.224 , 0. , 0.07466667,<br \/>\n0.01422222]), array([0. , 0.5625, 1.125 , 1.6875, 2.25 , 2.8125, 3.375 , 3.9375,<br \/>\n4.5 , 5.0625, 5.625 , 6.1875, 6.75 , 7.3125, 7.875 , 8.4375,<br \/>\n9. ]), &lt;a list of 16 Patch objects&gt;)<br \/>\n<strong><a href=\"https:\/\/data-flair.training\/blogs\/python-django-tutorial\/\" target=\"_blank\" rel=\"noopener\">Do you know about Python Django Tutorial For Beginners<\/a><\/strong><\/p>\n<pre class=\"EnlighterJSRAW\">&gt;&gt;&gt; plt.show()<\/pre>\n<div id=\"attachment_22352\" style=\"width: 573px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/bernoulli.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-22352\" class=\"wp-image-22352 size-full\" src=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/bernoulli.png\" alt=\"Python\u00a0Probability Distributions - Bernoulli\" width=\"563\" height=\"421\" srcset=\"https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/bernoulli.png 563w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/bernoulli-150x112.png 150w, https:\/\/data-flair.training\/blogs\/wp-content\/uploads\/sites\/2\/2018\/07\/bernoulli-300x224.png 300w\" sizes=\"auto, (max-width: 563px) 100vw, 563px\" \/><\/a><p id=\"caption-attachment-22352\" class=\"wp-caption-text\">Implement Python\u00a0Probability Distributions &#8211;\u00a0Bernoulli Distribution in Python<\/p><\/div>\n<p>So, this was all about Python Probability Distribution. Hope you like our explanation.<\/p>\n<h3 class=\"western\"><span style=\"font-size: x-large\">Conclusion<\/span><\/h3>\n<p>Hence, we studied Python Probability Distribution and its 4 types with an example. In addition, we learned how to implement these Python probability distributions. Furthermore, if you have any doubts, feel free to ask in the comments section.<\/p>\n<p>The normal distribution is the most common and appears as a bell curve. It is symmetric and centered around the mean. Many natural phenomena, like height, test scores, or errors in measurements, follow this distribution<\/p>\n<p>The binomial distribution models the number of successes in a fixed number of independent experiments. It is useful in scenarios like predicting the number of defective items in a batch or the number of heads in coin tosses. Python allows you to model this using binom.pmf() or generate samples using numpy.random.binomial(). The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space, such as the number of calls to a help center.<\/p>\n<p>The Bernoulli distribution is the simplest, dealing with binary outcomes\u2014success or failure, yes or no. It is the basis for logistic regression and classification tasks in machine learning.<\/p>\n<p>Related Topic- <strong><a href=\"https:\/\/data-flair.training\/blogs\/relational-database-with-python\/\">How to Work with Relational Database\u00a0<\/a><\/strong><br \/>\n<strong><a href=\"https:\/\/www.python.org\/\">For reference<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>After studying\u00a0Python Descriptive Statistics, now we are going to explore 4 Major Python Probability Distributions: Normal, Binomial, Poisson, and Bernoulli\u00a0Distributions in Python. Moreover, we will learn how to implement these Python probability distributions with&#46;&#46;&#46;<\/p>\n","protected":false},"author":5,"featured_media":22356,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[46],"tags":[1995,1996,16490,9108,9547,10721,10766,16024],"class_list":["post-22339","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-python","tag-binomial-distribution","tag-binomial-distribution-example","tag-implement-probability-distributions","tag-nominal-distributions-example","tag-poisson-distribution-example","tag-python-normal-distribution","tag-python-probability-distribution","tag-what-is-the-probability-distribution"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Probability Distributions in Python - Normal, Binomial, Poisson, Bernoulli - DataFlair<\/title>\n<meta name=\"description\" content=\"A probability distribution is a function under probability theory and statistics that gives us how probably are different outcomes.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/data-flair.training\/blogs\/python-probability-distributions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Probability Distributions in Python - 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