{"id":717,"date":"2023-07-29T00:10:17","date_gmt":"2023-07-29T00:10:17","guid":{"rendered":"https:\/\/statorials.org\/tr\/binom-dagilimi\/"},"modified":"2023-07-29T00:10:17","modified_gmt":"2023-07-29T00:10:17","slug":"binom-dagilimi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/binom-dagilimi\/","title":{"rendered":"Binom da\u011f\u0131l\u0131m\u0131na giri\u015f"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><script src=\"https:\/\/cdnjs.cloudflare.com\/ajax\/libs\/mathjs\/5.1.1\/math.js\"><\/script><script src=\"https:\/\/cdn.jsdelivr.net\/npm\/jstat@latest\/dist\/jstat.min.js\"><\/script><\/p>\n<style>\n@import url('https:\/\/fonts.googleapis.com\/css?family=Droid+Serif|Raleway');<\/p>\n<p>#words {\ncolor: black;\nfont-family: Raleway;\nmax-width: 550px;\nmargin: 25px auto;\nline-height: 1.75;\npadding-left: 100px;\n}<\/p>\n<p>#words label, input {\n    display: inline-block;\n    vertical-align: baseline;\n    width: 350px;\n}<\/p>\n<p>    #button {\n      border: 1px solid;\n      border-radius: 10px;\n      margin-top: 20px;\n      padding: 10px 10px;\n      cursor: pointer;\n      outline: none;\n      background-color: white;\n      color: black;\n      font-family: 'Work Sans', sans-serif;\n      border: 1px solid grey;\n      \/* Green *\/\n    }<\/p>\n<p>    #button:hover {\n      background-color: #f6f6f6;\n      border: 1px solid black;\n    }<\/p>\n<p>p, li {\n  color:#000000;\n  font-size: 19px;\n  font-family: 'Helvetica';\n}<\/p>\n<p>p a {\n  color: #9b59b6 !important;\n}\n<\/style>\n<p class=\"has-text-color\" style=\"color:#000000\"><strong>Binom da\u011f\u0131l\u0131m\u0131<\/strong> istatistikte en pop\u00fcler da\u011f\u0131l\u0131mlardan biridir. Binom da\u011f\u0131l\u0131m\u0131n\u0131 anlamak i\u00e7in \u00f6ncelikle <a href=\"https:\/\/statorials.org\/tr\/binom-deneyi\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"binomial experiments (opens in a new tab)\">binom deneylerini<\/a> anlamak yard\u0131mc\u0131 olur.<\/p>\n<h3 class=\"wp-block-heading\"> <strong>Binom deneyleri<\/strong><\/h3>\n<p> <strong>Binom deneyi<\/strong> a\u015fa\u011f\u0131daki \u00f6zelliklere sahip bir deneydir:<\/p>\n<ul>\n<li> Deney <em>n<\/em> tekrarlanan denemeden olu\u015fur.<\/li>\n<li> Her denemenin yaln\u0131zca iki olas\u0131 sonucu vard\u0131r.<\/li>\n<li> Ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 <em>p<\/em> ile g\u00f6sterilir, her deneme i\u00e7in ayn\u0131d\u0131r.<\/li>\n<li> Her test ba\u011f\u0131ms\u0131zd\u0131r.<\/li>\n<\/ul>\n<p> Binom deneyinin en belirgin \u00f6rne\u011fi yaz\u0131 tura atmakt\u0131r. \u00d6rne\u011fin, bir paray\u0131 10 kez havaya att\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m. Bu bir binom deneyidir \u00e7\u00fcnk\u00fc a\u015fa\u011f\u0131daki d\u00f6rt \u00f6zelli\u011fe sahiptir:<\/p>\n<ul>\n<li> Deney <em>n<\/em> tekrarlanan denemeden olu\u015fur \u2013 10 deneme vard\u0131r.<\/li>\n<li> Her denemenin yaln\u0131zca iki olas\u0131 sonucu vard\u0131r: yaz\u0131 veya tura.<\/li>\n<li> Ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 <em>p<\/em> ile g\u00f6sterilir, her deneme i\u00e7in ayn\u0131d\u0131r. Ba\u015far\u0131y\u0131 tura gelmek olarak tan\u0131mlarsak, ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 her deneme i\u00e7in tam olarak 0,5&#8217;tir.<\/li>\n<li> Her deneme ba\u011f\u0131ms\u0131zd\u0131r \u2013 Bir yaz\u0131 tura at\u0131\u015f\u0131n\u0131n sonucu, di\u011fer yaz\u0131 tura at\u0131\u015flar\u0131n\u0131n sonucunu etkilemez.<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"> <strong>Binom da\u011f\u0131l\u0131m\u0131<\/strong><\/h3>\n<p> <strong>Binom da\u011f\u0131l\u0131m\u0131,<\/strong> <em>n<\/em> binom deneyinde <em>k<\/em> ba\u015far\u0131 elde etme olas\u0131l\u0131\u011f\u0131n\u0131 tan\u0131mlar.<\/p>\n<p> E\u011fer bir <em>X<\/em> <a href=\"https:\/\/statorials.org\/tr\/rastgele-degiskenler\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"random variable (opens in a new tab)\">rastgele de\u011fi\u015fkeni<\/a> binom da\u011f\u0131l\u0131m\u0131n\u0131 takip ediyorsa, <em>X<\/em> = <em>k<\/em> ba\u015far\u0131s\u0131n\u0131n olas\u0131l\u0131\u011f\u0131 a\u015fa\u011f\u0131daki form\u00fclle bulunabilir:<\/p>\n<p> <strong>P(X=k) = <sub>n<\/sub> C <sub>k<\/sub> * p <sup>k<\/sup> * (1-p) <sup>nk<\/sup><\/strong><\/p>\n<p> Alt\u0131n:<\/p>\n<ul>\n<li> <strong>n:<\/strong> deneme say\u0131s\u0131<\/li>\n<li> <strong>k:<\/strong> ba\u015far\u0131 say\u0131s\u0131<\/li>\n<li> <strong>p:<\/strong> belirli bir denemede ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131<\/li>\n<li> <strong><sub>n<\/sub> C <sub>k<\/sub> :<\/strong> <em>n<\/em> denemede <em>k<\/em> ba\u015far\u0131 elde etmenin yollar\u0131n\u0131n say\u0131s\u0131<\/li>\n<\/ul>\n<p> \u00d6rnek: Bir paray\u0131 3 kez att\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m. Bu 3 at\u0131\u015fta 0, 1, 2 ve 3 tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in yukar\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/p>\n<p> <strong>P(X=0)<\/strong> = <sub>3<\/sub> C <sub>0<\/sub> * 0,5 <sup>0<\/sup> * (1-0,5) <sup>3-0<\/sup> = 1 * 1 * (0,5) <sup>3<\/sup> = <strong>0,125<\/strong><\/p>\n<p> <strong>P(X=1)<\/strong> = <sub>3<\/sub> C <sub>1<\/sub> * 0,5 <sup>1<\/sup> * (1-0,5) <sup>3-1<\/sup> = 3 * 0,5 * (0,5) <sup>2<\/sup> = <strong>0,375<\/strong><\/p>\n<p> <strong>P(X=2)<\/strong> = <sub>3<\/sub> C <sub>2<\/sub> * 0,5 <sup>2<\/sup> * (1-0,5) <sup>3-2<\/sup> = 3 * 0,25 * (0,5) <sup>1<\/sup> = <strong>0,375<\/strong><\/p>\n<p> <strong>P(X=3)<\/strong> = <sub>3<\/sub> C <sub>3<\/sub> * 0,5 <sup>3<\/sup> * (1-0,5) <sup>3-3<\/sup> = 1 * 0,125 * (0,5) <sup>0<\/sup> = <strong>0,125<\/strong><\/p>\n<p> <em>Not<\/em> <strong><em>:<\/em><\/strong> Her <sub><em>\u00f6rnekte<\/em><\/sub> <sub><em>nCk&#8217;yi<\/em><\/sub> <em>hesaplamak i\u00e7in bu birle\u015fik hesap makinesini kulland\u0131k<\/em> <em>.<\/em><\/p>\n<p> Bu olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6rselle\u015ftirmek i\u00e7in basit bir histogram olu\u015fturabiliriz: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/binomdist1.png\" alt=\"Binom da\u011f\u0131l\u0131m histogram\u0131\" class=\"wp-image-7153\" width=\"339\" height=\"335\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\"> <strong>K\u00fcm\u00fclatif binom olas\u0131l\u0131klar\u0131n\u0131n hesaplanmas\u0131<\/strong><\/h3>\n<p> Yukar\u0131daki form\u00fcl\u00fc kullanarak tek bir binom olas\u0131l\u0131\u011f\u0131n\u0131 (\u00f6rne\u011fin, 3 at\u0131\u015ftan 1&#8217;inde bir paran\u0131n tura gelme olas\u0131l\u0131\u011f\u0131) hesaplamak kolayd\u0131r, ancak k\u00fcm\u00fclatif binom olas\u0131l\u0131klar\u0131n\u0131 hesaplamak i\u00e7in bireysel olas\u0131l\u0131klar\u0131 toplamam\u0131z gerekir.<\/p>\n<p> \u00d6rne\u011fin, bir paran\u0131n 3 at\u0131\u015ftan 1&#8217;inde veya daha az\u0131nda tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimizi varsayal\u0131m. Bu olas\u0131l\u0131\u011f\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z:<\/p>\n<p> <strong>P(X\u22641)<\/strong> = P(X=0) + P(X=1) = 0,125 + 0,375 = <strong>0,5<\/strong> .<\/p>\n<p> Buna <strong>k\u00fcm\u00fclatif olas\u0131l\u0131k<\/strong> denir \u00e7\u00fcnk\u00fc birden fazla olas\u0131l\u0131\u011f\u0131n eklenmesini i\u00e7erir. Benzer bir form\u00fcl kullanarak her sonu\u00e7 i\u00e7in <em>k<\/em> veya daha az tura gelmenin k\u00fcm\u00fclatif olas\u0131l\u0131\u011f\u0131n\u0131 hesaplayabiliriz:<\/p>\n<p> <strong>P(X\u22640)<\/strong> = P(X=0) = <strong>0,125<\/strong> .<\/p>\n<p> <strong>P(X\u22641)<\/strong> = P(X=0) + P(X=1) = 0,125 + 0,375 = <strong>0,5<\/strong> .<\/p>\n<p> <strong>P(X\u22642)<\/strong> = P(X=0) + P(X=1) + P(X=2) = 0,125 + 0,375 + 0,375 = <strong>0,875<\/strong> .<\/p>\n<p> <strong>P(X\u22643)<\/strong> = P(X=0) + P(X=1) + P(X=2) + P(X=3) = 0,125 + 0,375 + 0,375 + 0,125 = <strong>1<\/strong> .<\/p>\n<p> Bu k\u00fcm\u00fclatif olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6rselle\u015ftirmek i\u00e7in bir histogram olu\u015fturabiliriz: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/binomdist2.png\" alt=\"K\u00fcm\u00fclatif binom olas\u0131l\u0131k da\u011f\u0131l\u0131m\u0131\" class=\"wp-image-7161\" width=\"346\" height=\"341\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h3 class=\"wp-block-heading\"> <strong>Binom Olas\u0131l\u0131k Hesaplay\u0131c\u0131s\u0131<\/strong><\/h3>\n<p> K\u00fc\u00e7\u00fck say\u0131larla \u00e7al\u0131\u015f\u0131rken (\u00f6rne\u011fin 3 yaz\u0131 tura at\u0131ld\u0131\u011f\u0131nda), binom olas\u0131l\u0131klar\u0131n\u0131 elle hesaplamak mant\u0131kl\u0131d\u0131r. Ancak daha b\u00fcy\u00fck say\u0131larla \u00e7al\u0131\u015ft\u0131\u011f\u0131m\u0131zda (\u00f6rne\u011fin 100 beraberlik), olas\u0131l\u0131klar\u0131 elle hesaplamak zor olabilir. Bu durumlarda a\u015fa\u011f\u0131daki gibi bir <strong>binom olas\u0131l\u0131k hesaplay\u0131c\u0131s\u0131n\u0131n<\/strong> kullan\u0131lmas\u0131 faydal\u0131 olabilir.<\/p>\n<p> \u00d6rne\u011fin, bir paray\u0131 n = 100 kez att\u0131\u011f\u0131m\u0131z\u0131, belirli bir denemede paran\u0131n tura gelme olas\u0131l\u0131\u011f\u0131n\u0131n p = 0,5 oldu\u011funu ve k = 43 kez veya daha az tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 bilmek istedi\u011fimizi varsayal\u0131m:<\/p>\n<div id=\"words\"> <label for=\"p\"><b>p<\/b> (belirli bir denemede ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131)<\/label><input id=\"p\" min=\"0\" type=\"number\" value=\"0.5\"><\/div>\n<div id=\"words\"> <label for=\"n\"><b>n<\/b> (deneme say\u0131s\u0131)<\/label><input id=\"n\" min=\"0\" type=\"number\" value=\"100\"><\/div>\n<div id=\"words\"> <label for=\"k\"><b>k<\/b> (ba\u015far\u0131 say\u0131s\u0131)<\/label> <input id=\"k\" min=\"0\" type=\"number\" value=\"43\"><\/div>\n<div id=\"words\"><input id=\"button\" type=\"button\" value=\"Calculate\" onclick=\"pvalue()\"><\/div>\n<div id=\"words\">\n<p> P(X= <span id=\"k1\">43<\/span> ) = <span id=\"exactProb\">0,03007<\/span><\/p>\n<p> P(X&lt; <span id=\"k2\">43<\/span> ) = <span id=\"lessProb\">0,06661<\/span><\/p>\n<p> P( <span id=\"k3\">X\u226443<\/span> ) = <span id=\"lessEProb\">0,09667<\/span><\/p>\n<p> P(X&gt; <span id=\"k4\">43<\/span> ) = <span id=\"greaterProb\">0,90333<\/span><\/p>\n<p> P( <span id=\"k5\">X\u226543<\/span> ) = <span id=\"greaterEProb\">0,93339<\/span><\/p>\n<\/div>\n<p><script><\/p>\n<p>function pvalue() {<\/p>\n<p>\/\/get input values\nvar p = document.getElementById('p').value*1;\nvar n = document.getElementById('n').value*1;\nvar k = document.getElementById('k').value*1;<\/p>\n<p>\/\/assign probabilities to variable names\nvar exactProb = jStat.binomial.pdf(k,n,p);\nvar lessProb = jStat.binomial.cdf(k-1,n,p);\nvar lessEProb = jStat.binomial.cdf(k,n,p);\nvar greaterProb = 1-jStat.binomial.cdf(k,n,p);\nvar greaterEProb = 1-jStat.binomial.cdf(k-1,n,p);<\/p>\n<p>\/\/output probabilities\ndocument.getElementById('k1').innerHTML = k;\ndocument.getElementById('k2').innerHTML = k;\ndocument.getElementById('k3').innerHTML = k;\ndocument.getElementById('k4').innerHTML = k;\ndocument.getElementById('k5').innerHTML = k;<\/p>\n<p>document.getElementById('exactProb').innerHTML = exactProb.toFixed(5);\ndocument.getElementById('lessProb').innerHTML = lessProb.toFixed(5);\ndocument.getElementById('lessEProb').innerHTML = lessEProb.toFixed(5);\ndocument.getElementById('greaterProb').innerHTML = greaterProb.toFixed(5);\ndocument.getElementById('greaterEProb').innerHTML = greaterEProb.toFixed(5);\n}\n<\/script><\/p>\n<p>Sonucun nas\u0131l yorumlanaca\u011f\u0131 a\u015fa\u011f\u0131da a\u00e7\u0131klanm\u0131\u015ft\u0131r:<\/p>\n<ul>\n<li> Paran\u0131n tam olarak 43 kez tura gelme olas\u0131l\u0131\u011f\u0131 <strong>0,03007&#8217;dir<\/strong> .<\/li>\n<li> Paran\u0131n 43 defadan az tura gelme olas\u0131l\u0131\u011f\u0131 <strong>0,06661&#8217;dir<\/strong> .<\/li>\n<li> Paran\u0131n 43 veya daha az kez tura gelme olas\u0131l\u0131\u011f\u0131 <strong>0,09667&#8217;dir<\/strong> .<\/li>\n<li> Paran\u0131n 43 defadan fazla tura gelme olas\u0131l\u0131\u011f\u0131 <strong>0,90333&#8217;t\u00fcr<\/strong> .<\/li>\n<li> Paran\u0131n 43 veya daha fazla kez tura gelme olas\u0131l\u0131\u011f\u0131 <strong>0,93339&#8217;dur<\/strong> .<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"> <strong>Binom da\u011f\u0131l\u0131m\u0131n\u0131n \u00f6zellikleri<\/strong><\/h3>\n<p> Binom da\u011f\u0131l\u0131m\u0131 a\u015fa\u011f\u0131daki \u00f6zelliklere sahiptir:<\/p>\n<p> Da\u011f\u0131l\u0131m\u0131n ortalamas\u0131 <strong>\u03bc = np&#8217;dir<\/strong><\/p>\n<p> Da\u011f\u0131l\u0131m\u0131n varyans\u0131: <strong>\u03c3<\/strong> <sup><strong>2<\/strong><\/sup> <strong>= np(1-p)<\/strong><\/p>\n<p> Da\u011f\u0131l\u0131m\u0131n standart sapmas\u0131 <strong>\u03c3 = \u221a<\/strong> <span style=\"text-decoration: overline;\"><strong>np(1-p)<\/strong><\/span><\/p>\n<p> \u00d6rnek: Bir paray\u0131 3 kez havaya att\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m. P = madalyonun tura gelme olas\u0131l\u0131\u011f\u0131 olsun.<\/p>\n<p> Bekledi\u011fimiz ortalama yaz\u0131 say\u0131s\u0131 \u03bc = np = 3*.5 = <strong>1.5&#8217;tir<\/strong> .<\/p>\n<p> Bekledi\u011fimiz ki\u015fi say\u0131s\u0131 varyans\u0131 \u03c3 <sup>2<\/sup> = np(1-p) = 3*.5*(1-.5) = <strong>0.75&#8217;tir<\/strong> .<\/p>\n<h3 class=\"wp-block-heading\"> <strong>Binom Da\u011f\u0131t\u0131m\u0131 Uygulama Problemleri<\/strong><\/h3>\n<p> Binom da\u011f\u0131l\u0131m\u0131 bilginizi test etmek i\u00e7in a\u015fa\u011f\u0131daki al\u0131\u015ft\u0131rma problemlerini kullan\u0131n.<\/p>\n<p> <strong>Sorun 1<\/strong><\/p>\n<p> <strong>Soru:<\/strong> Bob serbest at\u0131\u015f denemelerinin %60&#8217;\u0131n\u0131 yap\u0131yor. E\u011fer 12 serbest at\u0131\u015f yaparsa tam olarak 10 at\u0131\u015f yapma olas\u0131l\u0131\u011f\u0131 nedir?<\/p>\n<p> <strong>Cevap:<\/strong> Yukar\u0131daki p = 0,6, n = 12 ve k = 10 ile binom da\u011f\u0131l\u0131m hesaplay\u0131c\u0131s\u0131n\u0131 kullanarak P(X=10) = <strong>0,06385<\/strong> oldu\u011funu buluruz.<\/p>\n<p> <strong>Sorun 2<\/strong><\/p>\n<p> <strong>Soru:<\/strong> Jessica 5 kez yaz\u0131 tura at\u0131yor. Paran\u0131n 2 veya daha az kez tura gelme olas\u0131l\u0131\u011f\u0131 nedir?<\/p>\n<p> <strong>Cevap:<\/strong> Yukar\u0131daki p = 0,5, n = 5 ve k = 2 olan binom da\u011f\u0131l\u0131m hesaplay\u0131c\u0131s\u0131n\u0131 kullanarak P(X\u22642) = <strong>0,5<\/strong> oldu\u011funu buluruz.<\/p>\n<p> <strong>Sorun 3<\/strong><\/p>\n<p> <strong>Soru:<\/strong> Belirli bir \u00f6\u011frencinin belirli bir \u00fcniversiteye kabul edilme olas\u0131l\u0131\u011f\u0131 0,2&#8217;dir. 10 \u00f6\u011frenci ba\u015fvurursa 4&#8217;ten fazlas\u0131n\u0131n kabul edilme olas\u0131l\u0131\u011f\u0131 nedir?<\/p>\n<p> <strong>Cevap:<\/strong> Yukar\u0131daki p = 0,2, n = 10 ve k = 4 olan binom da\u011f\u0131l\u0131m hesaplay\u0131c\u0131s\u0131n\u0131 kullanarak P(X&gt;4) = <strong>0,03279&#8217;u<\/strong> buluruz.<\/p>\n<p> <strong>Sorun 4<\/strong><\/p>\n<p> <strong>Soru:<\/strong> Bir paray\u0131 12 kez at\u0131yorsunuz. Ortaya \u00e7\u0131kmas\u0131 beklenen ortalama kafa say\u0131s\u0131 nedir?<\/p>\n<p> <strong>Cevap:<\/strong> Binom da\u011f\u0131l\u0131m\u0131n\u0131n ortalamas\u0131n\u0131n \u03bc = np olarak hesapland\u0131\u011f\u0131n\u0131 hat\u0131rlay\u0131n. Yani \u03bc = 12*0,5 = <strong>6 yaz\u0131<\/strong> .<\/p>\n<p> <strong>Sorun 5<\/strong><\/p>\n<p> <strong>Soru:<\/strong> Mark denemelerinin %10&#8217;unda say\u0131 at\u0131yor. Belirli bir oyunda 5 deneme yaparsa, vurdu\u011fu home run say\u0131s\u0131ndaki fark nedir?<\/p>\n<p> <strong>Yan\u0131t:<\/strong> Binom da\u011f\u0131l\u0131m\u0131n\u0131n varyans\u0131n\u0131n \u03c3 <sup>2<\/sup> = np(1-p) \u015feklinde hesapland\u0131\u011f\u0131n\u0131 hat\u0131rlay\u0131n. B\u00f6ylece, <sup>\u03c32<\/sup> = 6*.1*(1-.1) = <strong>0.54<\/strong> .<\/p>\n<h3 class=\"wp-block-heading\"> <strong>Ek kaynaklar<\/strong><\/h3>\n<p> A\u015fa\u011f\u0131daki makaleler, binom da\u011f\u0131l\u0131m\u0131n\u0131 farkl\u0131 istatistiksel yaz\u0131l\u0131mlarda nas\u0131l kullanaca\u011f\u0131n\u0131z\u0131 \u00f6\u011frenmenize yard\u0131mc\u0131 olabilir:<\/p>\n<ul>\n<li> <a href=\"https:\/\/statorials.org\/tr\/binom-dagilimi-excel\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"How to calculate binomial probabilities in Excel (opens in a new tab)\">Excel&#8217;de Binom Olas\u0131l\u0131klar\u0131 Nas\u0131l Hesaplan\u0131r?<\/a><\/li>\n<li> <a href=\"https:\/\/statorials.org\/tr\/binom-olasiliklari-ti-84-hesaplayicisi\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"How to calculate binomial probabilities on a TI-84 calculator (opens in a new tab)\">TI-84 Hesap Makinesinde Binom Olas\u0131l\u0131klar\u0131 Nas\u0131l Hesaplan\u0131r?<\/a><\/li>\n<li> R&#8217;de binom olas\u0131l\u0131klar\u0131 nas\u0131l hesaplan\u0131r<\/li>\n<li> <a href=\"https:\/\/statorials.org\/tr\/binom-dagilimini-cizin-r\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\"How to plot a binomial distribution in R (opens in a new tab)\">R&#8217;de binom da\u011f\u0131l\u0131m\u0131 nas\u0131l \u00e7izilir<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Binom da\u011f\u0131l\u0131m\u0131 istatistikte en pop\u00fcler da\u011f\u0131l\u0131mlardan biridir. Binom da\u011f\u0131l\u0131m\u0131n\u0131 anlamak i\u00e7in \u00f6ncelikle binom deneylerini anlamak yard\u0131mc\u0131 olur. Binom deneyleri Binom deneyi a\u015fa\u011f\u0131daki \u00f6zelliklere sahip bir deneydir: Deney n tekrarlanan denemeden olu\u015fur. Her denemenin yaln\u0131zca iki olas\u0131 sonucu vard\u0131r. Ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 p ile g\u00f6sterilir, her deneme i\u00e7in ayn\u0131d\u0131r. Her test ba\u011f\u0131ms\u0131zd\u0131r. Binom deneyinin en belirgin \u00f6rne\u011fi [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-717","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Binom Da\u011f\u0131t\u0131m\u0131na Giri\u015f - Statorials<\/title>\n<meta name=\"description\" content=\"Resmi bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren binom da\u011f\u0131l\u0131m\u0131na basit bir giri\u015f.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/binom-dagilimi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Binom Da\u011f\u0131t\u0131m\u0131na Giri\u015f - Statorials\" \/>\n<meta property=\"og:description\" content=\"Resmi bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren binom da\u011f\u0131l\u0131m\u0131na basit bir giri\u015f.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/binom-dagilimi\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-29T00:10:17+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/binomdist1.png\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/binom-dagilimi\/\",\"url\":\"https:\/\/statorials.org\/tr\/binom-dagilimi\/\",\"name\":\"Binom Da\u011f\u0131t\u0131m\u0131na Giri\u015f - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-29T00:10:17+00:00\",\"dateModified\":\"2023-07-29T00:10:17+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Resmi bir tan\u0131m ve birka\u00e7 \u00f6rnek i\u00e7eren binom da\u011f\u0131l\u0131m\u0131na basit bir giri\u015f.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/binom-dagilimi\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/binom-dagilimi\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/binom-dagilimi\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Binom da\u011f\u0131l\u0131m\u0131na giri\u015f\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/tr\/#website\",\"url\":\"https:\/\/statorials.org\/tr\/\",\"name\":\"Statorials\",\"description\":\"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/tr\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"tr\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. 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