{"id":769,"date":"2023-07-28T20:00:37","date_gmt":"2023-07-28T20:00:37","guid":{"rendered":"https:\/\/statorials.org\/id\/distribusi-multinomial\/"},"modified":"2023-07-28T20:00:37","modified_gmt":"2023-07-28T20:00:37","slug":"distribusi-multinomial","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/distribusi-multinomial\/","title":{"rendered":"Pengantar distribusi multinomial"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Distribusi multinomial<\/strong> menggambarkan probabilitas diperolehnya sejumlah penghitungan tertentu untuk <em>k<\/em> hasil yang berbeda, ketika setiap hasil memiliki probabilitas terjadinya yang tetap.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sub>Jika<\/sub> <sub>suatu<\/sub> variabel <em>acak<\/em> <sub>_<\/sub> dapat dicari dengan rumus berikut:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Probabilitas =<\/strong> <strong>n! * (p <sub>1<\/sub> <sup>x <sub>1<\/sub><\/sup> * p <sub>2<\/sub> <sup>x <sub>2<\/sub><\/sup> * \u2026 * p <sub>k<\/sub> <sup>x <sub>k<\/sub><\/sup> ) \/ (x <sub>1<\/sub> ! * x <sub>2<\/sub> ! \u2026 * x <sub>k<\/sub> !)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Emas:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> jumlah total kejadian<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x <sub>1<\/sub> :<\/strong> berapa kali hasil 1 muncul<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p <sub>1<\/sub> :<\/strong> peluang munculnya hasil 1 pada suatu percobaan tertentu<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Misalnya ada 5 kelereng merah, 3 kelereng hijau, dan 2 kelereng biru dalam sebuah guci. Jika kita mengambil 5 kelereng secara acak dari dalam guci, dengan pengembalian, berapa peluang terambil tepat 2 kelereng merah, 2 kelereng hijau, dan 1 kelereng biru?<\/span><\/p>\n<p> <span style=\"color: #000000;\">Untuk menjawab pertanyaan tersebut, kita dapat menggunakan distribusi multinomial dengan parameter sebagai berikut:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> : 5<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x <sub>1<\/sub><\/strong> (# kelereng merah) = 2,<\/span> <span style=\"color: #000000;\"><strong>x <sub>2<\/sub><\/strong> (# kelereng hijau) = 2,<\/span> <span style=\"color: #000000;\"><strong>x <sub>3<\/sub><\/strong> (# kelereng biru) = 1<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p <sub>1<\/sub><\/strong> (masalah merah) = 0,5,<\/span> <span style=\"color: #000000;\"><strong>p <sub>2<\/sub><\/strong> (masalah hijau) = 0,3,<\/span> <span style=\"color: #000000;\"><strong>p <sub>3<\/sub><\/strong> (masalah biru) = 0,2<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Memasukkan angka-angka ini ke dalam rumus, kita menemukan bahwa probabilitasnya adalah:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Kemungkinan<\/strong> = 5! * (.5 <sup>2<\/sup> * .3 <sup>2<\/sup> * .2 <sup>1<\/sup> ) \/ (2! * 2! * 1!) = <strong>0,135<\/strong> .<\/span><\/p>\n<h2> <strong>Soal Praktek Distribusi Multinomial<\/strong><\/h2>\n<p> <span style=\"color: #000000;\">Gunakan soal latihan berikut untuk menguji pengetahuan Anda tentang distribusi multinomial.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em><strong>Catatan:<\/strong> Kami akan menggunakan <a href=\"https:\/\/statorials.org\/id\/kalkulator-distribusi-multinomial\/\" target=\"_blank\" rel=\"noopener\">Kalkulator Distribusi Multinomial<\/a> untuk menghitung jawaban atas pertanyaan-pertanyaan ini.<\/em><\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Masalah 1<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Pertanyaan:<\/strong> Dalam pemilihan walikota tiga arah, calon A memperoleh 10% suara, calon B memperoleh 40% suara, dan calon C memperoleh 50% suara. Jika kita mengambil sampel acak yang terdiri dari 10 pemilih, berapa peluang terambilnya 2 orang memilih calon A, 4 orang memilih calon B, dan 4 orang memilih calon C?<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>Jawaban:<\/strong> Menggunakan Kalkulator Distribusi Multinomial dengan input berikut, kita menemukan probabilitasnya adalah <strong>0,0504:<\/strong><\/span> <\/p>\n<p data-slot-rendered-dynamic=\"true\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8244 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/multinomialcalc1.png\" alt=\"Contoh Kalkulator Multinomial\" width=\"260\" height=\"553\" srcset=\"\" sizes=\"\"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Masalah 2<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Pertanyaan:<\/strong> Misalkan sebuah guci berisi 6 kelereng kuning, 2 kelereng merah, dan 2 kelereng merah muda. Jika kita mengambil 4 bola secara acak dari dalam guci, dengan pengembalian, berapa peluang terambilnya keempat bola tersebut berwarna kuning?<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>Jawaban:<\/strong> Menggunakan Kalkulator Distribusi Multinomial dengan input berikut, kita menemukan probabilitasnya adalah <strong>0,1296:<\/strong><\/span> <\/p>\n<p data-slot-rendered-dynamic=\"true\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8246 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/multinomialcalc2.png\" alt=\"Contoh Distribusi Probabilitas Multinomial\" width=\"261\" height=\"561\" srcset=\"\" sizes=\"\"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Masalah 3<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Pertanyaan:<\/strong> Misalkan dua siswa sedang bermain catur melawan satu sama lain. Peluang siswa A memenangkan suatu permainan adalah 0,5, peluang siswa B memenangkan permainan tertentu adalah 0,3, dan peluang terjadinya seri dalam suatu permainan adalah 0, 2. Jika mereka memainkan 10 permainan, berapakah peluang pemain A menang 4 kali, pemain B menang 5 kali, dan seri 1 kali?<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>Jawaban:<\/strong> Menggunakan Kalkulator Distribusi Multinomial dengan input berikut, kita menemukan probabilitasnya adalah <strong>0,038272:<\/strong><\/span> <\/p>\n<p data-slot-rendered-dynamic=\"true\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-8247 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/multinomialcalc3.png\" alt=\"Contoh Distribusi Multinomial\" width=\"259\" height=\"544\" srcset=\"\" sizes=\"\"><\/p>\n<h3 data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\"><strong>Sumber daya tambahan<\/strong><\/span><\/h3>\n<p data-slot-rendered-dynamic=\"true\"> <span style=\"color: #000000;\">Tutorial berikut memberikan pengenalan distribusi umum lainnya dalam statistik:<\/span><\/p>\n<p data-slot-rendered-dynamic=\"true\"> Pengenalan distribusi normal<br \/> <a href=\"https:\/\/statorials.org\/id\/distribusi-binomial-1\/\" target=\"_blank\" rel=\"noopener\">Pengenalan distribusi binomial<\/a><br \/> <a href=\"https:\/\/statorials.org\/id\/distribusi-ikan\/\" target=\"_blank\" rel=\"noopener\">Pengenalan distribusi Poisson<\/a><br \/> <a href=\"https:\/\/statorials.org\/id\/distribusi-geometris\/\" target=\"_blank\" rel=\"noopener\">Pengantar distribusi geometri<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Distribusi multinomial menggambarkan probabilitas diperolehnya sejumlah penghitungan tertentu untuk k hasil yang berbeda, ketika setiap hasil memiliki probabilitas terjadinya yang tetap. Jika suatu variabel acak _ dapat dicari dengan rumus berikut: Probabilitas = n! * (p 1 x 1 * p 2 x 2 * \u2026 * p k x k ) \/ (x 1 [&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":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Pengantar Distribusi Multinomial - Statologi<\/title>\n<meta name=\"description\" content=\"Pengenalan sederhana tentang distribusi multinomial, termasuk definisi formal dan beberapa contoh.\" \/>\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\/id\/distribusi-multinomial\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Pengantar Distribusi Multinomial - Statologi\" \/>\n<meta property=\"og:description\" content=\"Pengenalan sederhana tentang distribusi multinomial, termasuk definisi formal dan beberapa contoh.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/id\/distribusi-multinomial\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T20:00:37+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/multinomialcalc1.png\" \/>\n<meta name=\"author\" content=\"Benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/id\/distribusi-multinomial\/\",\"url\":\"https:\/\/statorials.org\/id\/distribusi-multinomial\/\",\"name\":\"Pengantar Distribusi Multinomial - Statologi\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/id\/#website\"},\"datePublished\":\"2023-07-28T20:00:37+00:00\",\"dateModified\":\"2023-07-28T20:00:37+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\"},\"description\":\"Pengenalan sederhana tentang distribusi multinomial, termasuk definisi formal dan beberapa contoh.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/id\/distribusi-multinomial\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/id\/distribusi-multinomial\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/id\/distribusi-multinomial\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/statorials.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Pengantar distribusi multinomial\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/id\/#website\",\"url\":\"https:\/\/statorials.org\/id\/\",\"name\":\"Statorials\",\"description\":\"Panduan anda untuk kompetensi statistik!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/id\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"id\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\",\"name\":\"Benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin anderson\"},\"description\":\"Halo, saya Benjamin, pensiunan profesor statistika yang menjadi guru Statorial yang berdedikasi. 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