{"id":554,"date":"2023-07-29T12:48:58","date_gmt":"2023-07-29T12:48:58","guid":{"rendered":"https:\/\/statorials.org\/tr\/binom-deneyi\/"},"modified":"2023-07-29T12:48:58","modified_gmt":"2023-07-29T12:48:58","slug":"binom-deneyi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/binom-deneyi\/","title":{"rendered":"Binom deneyleri: bir a\u00e7\u0131klama + \u00f6rnekler"},"content":{"rendered":"

<\/p>\n

\n

Binom deneylerini anlamak, binom da\u011f\u0131l\u0131m\u0131n\u0131<\/a> anlaman\u0131n ilk ad\u0131m\u0131d\u0131r.<\/span><\/p>\n

Bu e\u011fitimde bir binom deneyi tan\u0131mlan\u0131r ve binom deneyi olarak de\u011ferlendirilen<\/em> veya kabul edilmeyen<\/em> birka\u00e7 deney \u00f6rne\u011fi sunulur.<\/span><\/p>\n

Binom deneyi: tan\u0131m<\/strong><\/span><\/h2>\n

Binom deneyi<\/strong> a\u015fa\u011f\u0131daki d\u00f6rt \u00f6zelli\u011fe sahip bir deneydir:<\/span><\/p>\n

1. Deney n<\/em> tekrarlanan denemeden olu\u015fur.<\/strong> N<\/em> say\u0131s\u0131 herhangi bir miktarda olabilir. \u00d6rne\u011fin, bir paray\u0131 100 kez atarsak n<\/em> = 100 olur.<\/span><\/p>\n

2. Her denemenin yaln\u0131zca iki olas\u0131 sonucu vard\u0131r.<\/strong> Sonu\u00e7lar\u0131 genellikle “ba\u015far\u0131” veya “ba\u015far\u0131s\u0131zl\u0131k” olarak adland\u0131r\u0131r\u0131z, ancak “ba\u015far\u0131” yaln\u0131zca g\u00fcvendi\u011fimiz bir \u015feyin etiketidir. \u00d6rne\u011fin, bir yaz\u0131 tura att\u0131\u011f\u0131m\u0131zda yaz\u0131ya “vuru\u015f”, yaz\u0131ya da “ba\u015far\u0131s\u0131zl\u0131k” diyebiliriz.<\/span><\/p>\n

3. p<\/em> ile g\u00f6sterilen ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 her deneme i\u00e7in ayn\u0131d\u0131r.<\/strong> Bir deneyin ger\u00e7ek bir binom deneyi olabilmesi i\u00e7in “ba\u015far\u0131” olas\u0131l\u0131\u011f\u0131n\u0131n her denemede ayn\u0131 olmas\u0131 gerekir. \u00d6rne\u011fin, bir yaz\u0131 tura att\u0131\u011f\u0131m\u0131zda, her yaz\u0131 tura at\u0131\u015f\u0131m\u0131zda tura gelme (\u201cba\u015far\u0131\u201d) olas\u0131l\u0131\u011f\u0131 her zaman ayn\u0131d\u0131r.<\/span><\/p>\n

4. Her test ba\u011f\u0131ms\u0131zd\u0131r<\/strong> . Bu basit\u00e7e bir denemenin sonucunun ba\u015fka bir denemenin sonucunu etkilemedi\u011fi anlam\u0131na gelir. \u00d6rne\u011fin, bir paray\u0131 att\u0131\u011f\u0131m\u0131z\u0131 ve tura geldi\u011fini varsayal\u0131m. Tura gelmesi bir sonraki at\u0131\u015fta tura gelme olas\u0131l\u0131\u011f\u0131n\u0131 de\u011fi\u015ftirmez. Her \u00e7evirme (yani her \u201cdeneme\u201d) ba\u011f\u0131ms\u0131zd\u0131r.<\/span><\/p>\n

Binom deneylerine \u00f6rnekler<\/strong><\/span><\/h2>\n

A\u015fa\u011f\u0131daki deneylerin t\u00fcm\u00fc binom deneylerinin \u00f6rnekleridir.<\/span><\/p>\n

\u00f6rnek 1<\/strong><\/span><\/h3>\n

Bir paray\u0131 10 kez \u00e7evirin. Ka\u00e7 kez kuyruk d\u00fc\u015ft\u00fc\u011f\u00fcn\u00fc kaydedin.<\/strong><\/span><\/em><\/p>\n

Bu bir binom deneyidir \u00e7\u00fcnk\u00fc a\u015fa\u011f\u0131daki d\u00f6rt \u00f6zelli\u011fe sahiptir:<\/span><\/p>\n

    \n
  • Deney n<\/em> tekrarlanan denemeden olu\u015fur.<\/strong> Bu durumda 10 deneme yap\u0131l\u0131r.<\/span><\/li>\n
  • Her denemenin yaln\u0131zca iki olas\u0131 sonucu vard\u0131r.<\/strong> Madeni para yaln\u0131zca yaz\u0131 veya tura gelebilir.<\/span><\/li>\n
  • Ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 her deneme i\u00e7in ayn\u0131d\u0131r<\/strong> . Ba\u015far\u0131y\u0131 kafan\u0131za \u00e7arpmak olarak tan\u0131mlarsak, her denemede ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 tam olarak 0,5’tir.<\/span><\/li>\n
  • Her test ba\u011f\u0131ms\u0131zd\u0131r<\/strong> . Bir \u00e7ekili\u015fin sonucu di\u011fer \u00e7ekili\u015fin sonucunu etkilemez.<\/span><\/li>\n<\/ul>\n

    \u00d6rnek #2<\/strong><\/span><\/h3>\n

    6 tarafl\u0131 adil bir zar\u0131 20 kez at\u0131n. 2’nin ka\u00e7 kez g\u00f6r\u00fcnd\u00fc\u011f\u00fcn\u00fc kaydedin.<\/strong><\/span><\/em><\/p>\n

    Bu bir binom deneyidir \u00e7\u00fcnk\u00fc a\u015fa\u011f\u0131daki d\u00f6rt \u00f6zelli\u011fe sahiptir:<\/span><\/p>\n

      \n
    • Deney n<\/em> tekrarlanan denemeden olu\u015fur.<\/strong> Bu durumda 20 deneme vard\u0131r.<\/span><\/li>\n
    • Her denemenin yaln\u0131zca iki olas\u0131 sonucu vard\u0131r.<\/strong> 2’yi “ba\u015far\u0131” olarak tan\u0131mlarsak, zar her seferinde ya 2’ye (ba\u015far\u0131) ya da ba\u015fka bir say\u0131ya (ba\u015far\u0131s\u0131zl\u0131k) denk gelir.<\/span><\/li>\n
    • Ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 her deneme i\u00e7in ayn\u0131d\u0131r<\/strong> . Her denemede zar\u0131n 2’ye gelme olas\u0131l\u0131\u011f\u0131 1\/6’d\u0131r. Bu olas\u0131l\u0131k bir denemeden di\u011ferine de\u011fi\u015fmez.<\/span><\/li>\n
    • Her test ba\u011f\u0131ms\u0131zd\u0131r<\/strong> . Bir kal\u0131p at\u0131\u015f\u0131n\u0131n sonucu di\u011fer kal\u0131p at\u0131\u015flar\u0131n\u0131n sonucunu etkilemez.<\/span><\/li>\n<\/ul>\n

      \u00d6rnek #3<\/strong><\/span><\/h3>\n

      Tyler serbest at\u0131\u015f denemelerinin %70’ini yap\u0131yor. 15 deneme yapt\u0131\u011f\u0131n\u0131 varsayal\u0131m. Yapt\u0131\u011f\u0131 sepet say\u0131s\u0131n\u0131 kaydedin.<\/strong><\/span><\/em><\/p>\n

      Bu bir binom deneyidir \u00e7\u00fcnk\u00fc a\u015fa\u011f\u0131daki d\u00f6rt \u00f6zelli\u011fe sahiptir:<\/span><\/p>\n

        \n
      • Deney n<\/em> tekrarlanan denemeden olu\u015fur.<\/strong> Bu durumda 15 deneme vard\u0131r.<\/span><\/li>\n
      • Her denemenin yaln\u0131zca iki olas\u0131 sonucu vard\u0131r.<\/strong> Tyler her denemede ya basketi at\u0131yor ya da \u0131skal\u0131yor.<\/span><\/li>\n
      • Ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131 her deneme i\u00e7in ayn\u0131d\u0131r<\/strong> . Her denemede Tyler’\u0131n basket atma olas\u0131l\u0131\u011f\u0131 %70’tir. Bu olas\u0131l\u0131k bir denemeden di\u011ferine de\u011fi\u015fmez.<\/span><\/li>\n
      • Her test ba\u011f\u0131ms\u0131zd\u0131r<\/strong> . Bir serbest at\u0131\u015f giri\u015fiminin sonucu, di\u011fer herhangi bir serbest at\u0131\u015f giri\u015fiminin sonucunu etkilemez.<\/span><\/li>\n<\/ul>\n

        Binom deneyleri olmayan<\/em> \u00f6rnekler<\/strong><\/span><\/h2>\n

        \u00f6rnek 1<\/strong><\/span><\/h3>\n

        100 ki\u015fiye ka\u00e7 ya\u015f\u0131nda olduklar\u0131n\u0131 sorun<\/strong><\/span><\/em> .<\/strong><\/span><\/p>\n

        Bu bir binom deneyi de\u011fil<\/em> \u00e7\u00fcnk\u00fc ikiden fazla olas\u0131 sonu\u00e7 var.<\/span><\/p>\n

        \u00d6rnek #2<\/strong><\/span><\/h3>\n

        5 g\u00f6r\u00fcnene kadar 6 tarafl\u0131 adil bir zar at\u0131n.<\/i><\/b><\/span><\/p>\n

        Bu bir binom deneyi de\u011fildir<\/em> \u00e7\u00fcnk\u00fc \u00f6nceden tan\u0131mlanm\u0131\u015f n<\/em> say\u0131da deneme yoktur. 5 g\u00f6r\u00fcnene kadar ka\u00e7 at\u0131\u015f yap\u0131lmas\u0131 gerekti\u011fi hakk\u0131nda hi\u00e7bir fikrimiz yok.<\/span><\/p>\n

        \u00d6rnek #3<\/strong><\/span><\/h3>\n

        Bir kart destesinden 5 kart \u00e7ekin.<\/i><\/b><\/span><\/p>\n

        Bu bir binom deneyi de\u011fildir<\/em> \u00e7\u00fcnk\u00fc bir denemenin sonucu (\u00f6rne\u011fin desteden belirli bir kart\u0131n \u00e7ekilmesi) sonraki denemelerin sonucunu etkiler.<\/span><\/p>\n

        Binom deneyinin bir \u00f6rne\u011fi ve \u00e7\u00f6z\u00fcm\u00fc<\/strong><\/span><\/h2>\n

        A\u015fa\u011f\u0131daki \u00f6rnek, binom deneyiyle ilgili bir sorunun nas\u0131l \u00e7\u00f6z\u00fclece\u011fini g\u00f6sterir.<\/span><\/p>\n

        Bir paray\u0131 10 kez atars\u0131n\u0131z. Paran\u0131n tam olarak 7 tura gelme olas\u0131l\u0131\u011f\u0131 nedir?<\/em><\/strong><\/span><\/p>\n

        Bir binom deneyinde n<\/em> ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131n\u0131 bulmak istedi\u011fimizde a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanmam\u0131z gerekir:<\/span><\/p>\n

        P(tam olarak k<\/em> ba\u015far\u0131) = n<\/sub> C k<\/sub> * p k<\/sup> * (1-p) nk<\/sup><\/span><\/p>\n

        Alt\u0131n:<\/span><\/p>\n

          \n
        • n:<\/strong> deneme say\u0131s\u0131<\/span><\/li>\n
        • k:<\/strong> ba\u015far\u0131 say\u0131s\u0131<\/span><\/li>\n
        • C:<\/strong> \u201ckombinasyon\u201d sembol\u00fc<\/span><\/li>\n
        • p:<\/strong> belirli bir denemede ba\u015far\u0131 olas\u0131l\u0131\u011f\u0131<\/span><\/li>\n<\/ul>\n

          Bu say\u0131lar\u0131 form\u00fcle yerle\u015ftirerek \u015funu elde ederiz:<\/span><\/p>\n

          P(7 kafa) = 10<\/sub> C 7<\/sub> * 0,5 7<\/sup> * (1-0,5) 10-7<\/sup> = (120) * (0,0078125) * (0,125) = 0,11719<\/strong> .<\/span><\/p>\n

          Yani madalyonun 7 kez tura gelme olas\u0131l\u0131\u011f\u0131 0,11719’dur<\/strong> .<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

          Binom deneylerini anlamak, binom da\u011f\u0131l\u0131m\u0131n\u0131 anlaman\u0131n ilk ad\u0131m\u0131d\u0131r. Bu e\u011fitimde bir binom deneyi tan\u0131mlan\u0131r ve binom deneyi olarak de\u011ferlendirilen veya kabul edilmeyen birka\u00e7 deney \u00f6rne\u011fi sunulur. Binom deneyi: tan\u0131m Binom deneyi a\u015fa\u011f\u0131daki d\u00f6rt \u00f6zelli\u011fe sahip bir deneydir: 1. Deney n tekrarlanan denemeden olu\u015fur. N say\u0131s\u0131 herhangi bir miktarda olabilir. \u00d6rne\u011fin, bir paray\u0131 100 kez atarsak […]<\/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-554","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"\nBinom deneyleri: bir a\u00e7\u0131klama + \u00f6rnekler - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde birka\u00e7 \u00f6rnekle birlikte binom deneyinin tan\u0131m\u0131 sa\u011flanmaktad\u0131r.\" \/>\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-deneyi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Binom deneyleri: bir a\u00e7\u0131klama + \u00f6rnekler - Statorials\" \/>\n<meta property=\"og:description\" content=\"Bu e\u011fitimde birka\u00e7 \u00f6rnekle birlikte binom deneyinin tan\u0131m\u0131 sa\u011flanmaktad\u0131r.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/binom-deneyi\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-29T12:48:58+00:00\" \/>\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=\"4 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/binom-deneyi\/\",\"url\":\"https:\/\/statorials.org\/tr\/binom-deneyi\/\",\"name\":\"Binom deneyleri: bir a\u00e7\u0131klama + \u00f6rnekler - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-29T12:48:58+00:00\",\"dateModified\":\"2023-07-29T12:48:58+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Bu e\u011fitimde birka\u00e7 \u00f6rnekle birlikte binom deneyinin tan\u0131m\u0131 sa\u011flanmaktad\u0131r.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/binom-deneyi\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/binom-deneyi\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/binom-deneyi\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Binom deneyleri: bir a\u00e7\u0131klama + \u00f6rnekler\"}]},{\"@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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