{"id":1023,"date":"2023-07-27T23:10:51","date_gmt":"2023-07-27T23:10:51","guid":{"rendered":"https:\/\/statorials.org\/id\/koefisien-multinomial\/"},"modified":"2023-07-27T23:10:51","modified_gmt":"2023-07-27T23:10:51","slug":"koefisien-multinomial","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/koefisien-multinomial\/","title":{"rendered":"Koefisien multinomial: definisi & contoh"},"content":{"rendered":"

<\/p>\n

\n

Koefisien multinomial<\/strong> menjelaskan banyaknya kemungkinan partisi dari n<\/em> objek menjadi k<\/em> kelompok berukuran n 1<\/sub><\/em> , n 2<\/sub><\/em> , \u2026, n k<\/sub><\/em> .<\/span><\/p>\n

Rumus untuk menghitung koefisien multinomial adalah:<\/span><\/p>\n

Koefisien multinomial = n! \/ (n 1<\/sub> ! * n 2<\/sub> ! * \u2026 * nk<\/sub> !)<\/span><\/p>\n

Contoh berikut mengilustrasikan cara menghitung koefisien multinomial dalam praktiknya.<\/span><\/p>\n

Contoh 1: huruf dalam sebuah kata<\/strong><\/span><\/h3>\n

Ada berapa partisi unik dari kata ARKANSAS?<\/span><\/p>\n

Solusi:<\/strong> Kita cukup memasukkan nilai berikut ke dalam rumus koefisien multinomial:<\/span><\/p>\n

n<\/strong> (jumlah huruf): 8<\/span><\/p>\n

n 1<\/sub><\/strong> (huruf \u201cA\u201d): 3<\/span><\/p>\n

n 2<\/sub><\/strong> (huruf \u201cR\u201d): 1<\/span><\/p>\n

n 3<\/sub><\/strong> (huruf \u201cK\u201d): 1<\/span><\/p>\n

n 4<\/sub><\/strong> (huruf \u201cN\u201d): 1<\/span><\/p>\n

n 5<\/sub><\/strong> (huruf \u201cS\u201d): 2<\/span><\/p>\n

Koefisien multinomial = 8! \/ (3! * 1! * 1! * 1! * 2!) = 3,360<\/strong><\/span><\/p>\n

Ada 3.360<\/strong> partisi unik dari kata ARKANSAS.<\/span><\/p>\n

Contoh 2: Siswa per tahun ajaran<\/strong><\/span><\/h3>\n

Sekelompok enam siswa terdiri dari 3 senior, 2 junior dan 1 mahasiswa tingkat dua. Berapa banyak skor unik yang diperoleh dari kelompok siswa ini per tingkat?<\/span><\/p>\n

Solusi:<\/strong> Kita cukup memasukkan nilai berikut ke dalam rumus koefisien multinomial:<\/span><\/p>\n

n<\/strong> (jumlah siswa): 6<\/span><\/p>\n

n 1<\/sub><\/strong> (jumlah senior): 3<\/span><\/p>\n

n 2<\/sub><\/strong> (jumlah junior): 2<\/span><\/p>\n

n 3<\/sub><\/strong> (jumlah siswa tahun kedua): 1<\/span><\/p>\n

Koefisien multinomial = 6! \/ (3! * 2! * 1!) = 60<\/strong><\/span><\/p>\n

Ada 60<\/strong> skor unik dari siswa ini per level.<\/span><\/p>\n

Contoh 3: Preferensi partai politik<\/strong><\/span><\/h3>\n

Dari sepuluh penduduk di suatu daerah, 3 orang adalah Partai Republik, 5 orang Demokrat, dan 2 orang independen. Berapa banyak partisi unik yang ada pada kelompok penduduk ini berdasarkan partai politik?<\/span><\/p>\n

Solusi:<\/strong> Kita cukup memasukkan nilai berikut ke dalam rumus koefisien multinomial:<\/span><\/p>\n

n<\/strong> (jumlah penduduk): 10<\/span><\/p>\n

n 1<\/sub><\/strong> (total Partai Republik): 3<\/span><\/p>\n

Nomor 2<\/sub><\/strong> (total Demokrat): 5<\/span><\/p>\n

n 3<\/sub><\/strong> (jumlah Independen): 2<\/span><\/p>\n

Koefisien multinomial = 10! \/ (3! * 5! * 2!) = 2,520<\/strong><\/span><\/p>\n

Ada 2.520<\/strong> pengelompokan unik penduduk ini berdasarkan partai politik.<\/span><\/p>\n

Sumber daya tambahan<\/strong><\/span><\/h3>\n

Koefisien multinomial digunakan sebagai bagian dari rumus distribusi multinomial<\/a> , yang mendeskripsikan probabilitas diperolehnya sejumlah hitungan tertentu untuk k<\/em> hasil yang berbeda, ketika setiap hasil memiliki probabilitas terjadinya yang tetap.<\/span><\/p>\n

Bonus:<\/strong> Anda dapat menggunakan Kalkulator Koefisien Multinomial untuk menghitung koefisien multinomial dengan mudah.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Koefisien multinomial menjelaskan banyaknya kemungkinan partisi dari n objek menjadi k kelompok berukuran n 1 , n 2 , \u2026, n k . Rumus untuk menghitung koefisien multinomial adalah: Koefisien multinomial = n! \/ (n 1 ! * n 2 ! * \u2026 * nk !) Contoh berikut mengilustrasikan cara menghitung koefisien multinomial dalam praktiknya. […]<\/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":"\nKoefisien multinomial: definisi dan contoh - Statologi<\/title>\n<meta name=\"description\" content=\"Penjelasan sederhana tentang koefisien multinomial, beserta definisi dan beberapa contohnya.\" \/>\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\/koefisien-multinomial\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Koefisien multinomial: definisi dan contoh - Statologi\" \/>\n<meta property=\"og:description\" content=\"Penjelasan sederhana tentang koefisien multinomial, beserta definisi dan beberapa contohnya.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/id\/koefisien-multinomial\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-27T23:10:51+00:00\" \/>\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=\"1 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/id\/koefisien-multinomial\/\",\"url\":\"https:\/\/statorials.org\/id\/koefisien-multinomial\/\",\"name\":\"Koefisien multinomial: definisi dan contoh - Statologi\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/id\/#website\"},\"datePublished\":\"2023-07-27T23:10:51+00:00\",\"dateModified\":\"2023-07-27T23:10:51+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\"},\"description\":\"Penjelasan sederhana tentang koefisien multinomial, beserta definisi dan beberapa contohnya.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/id\/koefisien-multinomial\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/id\/koefisien-multinomial\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/id\/koefisien-multinomial\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/statorials.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Koefisien multinomial: definisi & contoh\"}]},{\"@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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