{"id":233,"date":"2023-08-03T20:59:59","date_gmt":"2023-08-03T20:59:59","guid":{"rendered":"https:\/\/statorials.org\/id\/distribusi-binomial-negatif-1\/"},"modified":"2023-08-03T20:59:59","modified_gmt":"2023-08-03T20:59:59","slug":"distribusi-binomial-negatif-1","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/distribusi-binomial-negatif-1\/","title":{"rendered":"Distribusi binomial negatif"},"content":{"rendered":"<p>Artikel ini menjelaskan apa itu distribusi binomial negatif dan kegunaannya. Anda juga akan menemukan rumus distribusi binomial negatif, contoh nyata dan sifat-sifat distribusi probabilitas jenis ini. Terakhir, Anda dapat menghitung probabilitas distribusi binomial negatif dengan kalkulator online. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-binomial-negativa\"><\/span> Berapakah distribusi binomial negatif?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Distribusi binomial negatif<\/strong> adalah distribusi probabilitas yang menggambarkan jumlah percobaan Bernoulli yang diperlukan untuk memperoleh sejumlah hasil positif.<\/p>\n<p> Oleh karena itu, distribusi binomial negatif memiliki dua parameter karakteristik: <em>r<\/em> adalah jumlah hasil sukses yang diinginkan dan <em>p<\/em> adalah probabilitas keberhasilan setiap percobaan Bernoulli yang dilakukan.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-171122de529a1c006bc46e8d89176016_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim \\text{BN}(r,p)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Ingatlah bahwa uji Bernoulli adalah eksperimen yang mempunyai dua kemungkinan hasil: &#8220;berhasil&#8221; dan &#8220;gagal&#8221;. Jadi jika peluang \u201cberhasil\u201d adalah <em>p<\/em> , peluang \u201cgagal\u201d adalah <em>q=1-p<\/em> .<\/p>\n<p> Jadi, distribusi binomial negatif mendefinisikan suatu proses di mana percobaan Bernoulli dilakukan sebanyak yang diperlukan untuk mendapatkan <em>hasil<\/em> yang positif. Selain itu, semua uji coba Bernoulli ini bersifat independen dan memiliki kemungkinan <em>keberhasilan<\/em> yang konstan.<\/p>\n<p> Misalnya, variabel acak yang mengikuti distribusi binomial negatif adalah berapa kali sebuah dadu harus dilempar hingga angka 6 dilempar tiga kali.<\/p>\n<p> Perbedaan antara distribusi binomial negatif dan distribusi binomial adalah distribusi binomial negatif menghitung berapa kali yang diperlukan untuk mendapatkan sejumlah hasil yang berhasil, sedangkan distribusi binomial menghitung jumlah kasus yang berhasil dalam serangkaian uji Bernoulli. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Lihat:<\/strong> <a href=\"https:\/\/statorials.org\/id\/distribusi-binomial-1\/\">Apa yang dimaksud dengan distribusi binomial?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-binomial-negativa\"><\/span> Rumus distribusi binomial negatif<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Mengingat parameter <em>r, p, x,<\/em> probabilitas distribusi binomial negatif dihitung dengan mengalikan bilangan kombinatorial <em>x-1<\/em> dalam <em>xr<\/em> dengan <em>(1-p) <sup>xr<\/sup><\/em> dengan <em>p <sup>r<\/sup><\/em> .<\/p>\n<p> Jadi, <strong>rumus menghitung probabilitas distribusi binomial negatif<\/strong> adalah: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/formule-de-distribution-binomiale-negative.png\" alt=\"Rumus distribusi binomial negatif\" class=\"wp-image-4813\" width=\"318\" height=\"319\" srcset=\"\" sizes=\"\"><\/figure>\n<p> \ud83d\udc49 <u style=\"text-decoration-color:#FF8A05;\">Anda dapat menggunakan kalkulator di bawah ini untuk menghitung peluang suatu variabel yang mengikuti distribusi binomial negatif.<\/u> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicio-resuelto-de-la-distribucion-binomial-negativa\"><\/span> Latihan terpecahkan dari distribusi binomial negatif<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li> Berapa peluang sebuah mata uang dilempar delapan kali dan muncul gambar keempat kalinya pada pelemparan kedelapan?<\/li>\n<\/ul>\n<p> Pertama, kita perlu menghitung peluang munculnya kepala saat melempar koin. Dalam hal ini, kita hanya mempunyai satu hasil positif (head) dari dua kemungkinan hasil (head dan tail), sehingga peluang suksesnya adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bdceac6409b69d142f23801ec85e2691_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p=\\cfrac{1}{2}=0,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"93\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Jadi, variabel acak dalam soal ini mengikuti distribusi binomial negatif di mana r=4 dan p=0,5. Oleh karena itu, kami menggunakan rumus distribusi binomial negatif untuk menghitung probabilitas yang diminta oleh latihan tersebut. <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bc56100604e5889a6d169c0395f19ebe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P[X=x]&amp;=\\begin{pmatrix}x-1\\\\ x-r\\end{pmatrix}\\cdot (1-p)^{x-r}\\cdot p^r\\\\[2ex]\\displaystyle P[X=8]&amp;=\\begin{pmatrix}8-1\\\\ 8-4\\end{pmatrix}\\cdot (1-0,5)^{8-4}\\cdot 0,5^4\\\\[2ex] P[X=8]&amp;=0,1367\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"151\" width=\"316\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-binomial-negativa\"><\/span> Ciri-ciri distribusi binomial negatif<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Di bawah ini adalah ciri-ciri terpenting dari distribusi binomial negatif.<\/p>\n<ul>\n<li> Distribusi binomial negatif ditentukan oleh dua parameter karakteristik: <em>r<\/em> adalah jumlah hasil sukses yang diinginkan dan <em>p<\/em> adalah probabilitas keberhasilan setiap percobaan Bernoulli yang dilakukan.<\/li>\n<\/ul>\n<pre class=\"ql-errors\"> *** QuickLaTeX cannot compile formula:\n\\begin{array}{c}r\\in \\mathbb{Z}^+ \\\\[2ex] 0 &lt;ul&gt;&lt;li&gt; The mean of the negative binomial distribution is equal to &lt;em&gt;r&lt;\/em&gt; multiplied by &lt;em&gt;(1-p)&lt;\/em&gt; and divided by &lt;em&gt;p&lt;\/em&gt; . Thus the formula which makes it possible to calculate the mean of a negative binomial distribution is the following: &lt;\/li&gt;&lt;\/ul&gt;[latex]E[X]=\\cfrac{r\\cdot (1-p)}{p}\n\n*** Error message:\nMissing $ inserted.\nleading text: \\begin{array}{c}\nPlease use \\mathaccent for accents in math mode.\nleading text: ...The mean of the binomial distribution born\nPlease use \\mathaccent for accents in math mode.\nleading text: ... the negative binomial distribution is\nPlease use \\mathaccent for accents in math mode.\nleading text: ...negative binomial distribution is equal to\nPlease use \\mathaccent for accents in math mode.\nleading text: ...gative is equal to &lt;em&gt;r&lt;\/em&gt; multiplied\nPlease use \\mathaccent for accents in math mode.\nleading text: ...m&gt; multiplied by &lt;em&gt;(1-p)&lt;\/em&gt; and divided\nPlease use \\mathaccent for accents in math mode.\nleading text: ...the mean of a binomial distribution born\n\\begin{array} on input line 8 ended by \\end{document}.\n\n<\/pre>\n<ul>\n<li> Varians dari distribusi binomial negatif sama dengan <em>r<\/em> dikalikan <em>(1-p)<\/em> dibagi <em>p <sup>2<\/sup><\/em> .<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c82d66018d0715f20318f383cf7c04c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=\\cfrac{r\\cdot (1-p)}{p^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"163\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<ul>\n<li> Jika parameter <em>r<\/em> lebih besar dari 1, modus distribusi binomial negatif dapat dihitung dengan rumus berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-600d3f94b3cd3927f264450bcd043a86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\lfloor \\frac{(r-1)(1-p)}{p}\\rfloor\\quad \\text{para }r>1&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;42&#8243; width=&#8221;221&#8243; style=&#8221;vertical-align: -16px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Fungsi massa yang memungkinkan untuk menentukan probabilitas distribusi binomial negatif adalah sebagai berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-beafc8c08e7aad51059349dfd2addd5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P[X=x]=\\begin{pmatrix}x-1\\\\ x-r\\end{pmatrix}\\cdot (1-p)^{x-r}\\cdot p^r\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"284\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> Koefisien skewness dari distribusi binomial negatif dihitung dengan ekspresi berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9bc0a97cdf77d4dd439c71cf8637e53c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\frac{2-p}{\\sqrt{r\\,(1-p)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"122\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<ul>\n<li> Kurtosis distribusi binomial negatif dapat dicari dengan rumus berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-510199601f8ac60aa64008f00d959562_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C=\\frac{6}{r} + \\frac{p^2}{r\\,(1-p)}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"139\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> Jika parameter <em>r<\/em> sama dengan 1, maka kita mempunyai kasus <a href=\"https:\/\/statorials.org\/id\/distribusi-geometris\/\">distribusi geometri<\/a> . <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-24bb5ef017a69a1a9de1e07f32412fcc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r=1 \\quad\\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad X\\sim \\text{Geometrica}(p)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"350\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-de-la-distribucion-binomial-negativa\"><\/span> Kalkulator Distribusi Binomial Negatif<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Masukkan nilai parameter <em>r, p, x<\/em> ke dalam kalkulator berikut untuk menghitung probabilitas. Anda harus memasukkan angka menggunakan titik sebagai pemisah desimal, misalnya 0,50.<\/p>\n<form action=\"\" method=\"post\">\n<div style=\"margin-bottom:20px; margin-left:5%\"> <span style=\"color:#101010;font-weight: normal;\"><span style=\"color:#1C2C92\"><strong>\u27a4<\/strong><\/span> Jumlah hasil yang berhasil <span style=\"color:#1C2C92\"><strong>\u2192<\/strong><\/span><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-2060a909f2905bcbe83f8fe9152c2284_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r = \" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"26\" style=\"vertical-align: 0px;\"><\/p>\n<p><\/span> <input name=\"r\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce el valor de r aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/div>\n<div style=\"margin-bottom:20px; margin-left:5%\"> <span style=\"color:#101010;font-weight: normal;\"><span style=\"color:#1C2C92\"><strong>\u27a4<\/strong><\/span> Probabilitas keberhasilan setiap percobaan <span style=\"color:#1C2C92\"><strong>\u2192<\/strong><\/span><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e67f693705a2e492d8981f0ed1387c3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p = \" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"28\" style=\"vertical-align: -4px;\"><\/p>\n<p><\/span> <input name=\"prob\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce el valor de p aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/div>\n<div style=\"margin-bottom:20px; margin-left:5%\"> <span style=\"color:#101010;font-weight: normal;\"><span style=\"color:#1C2C92\"><strong>\u27a4<\/strong><\/span> Jumlah total percobaan yang dilakukan <span style=\"color:#1C2C92\"><strong>\u2192<\/strong><\/span><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-04ae6e91e4423afa96cc9b717c007c88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x = \" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"28\" style=\"vertical-align: 0px;\"><\/p>\n<p><\/span> <input name=\"xigual\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce el valor de x aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/div>\n<div style=\"text-align:center\"><input align=\"center\" style=\"border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"Hitung probabilitasnya\"><\/div>\n<\/form>\n","protected":false},"excerpt":{"rendered":"<p>Artikel ini menjelaskan apa itu distribusi binomial negatif dan kegunaannya. Anda juga akan menemukan rumus distribusi binomial negatif, contoh nyata dan sifat-sifat distribusi probabilitas jenis ini. Terakhir, Anda dapat menghitung probabilitas distribusi binomial negatif dengan kalkulator online. Berapakah distribusi binomial negatif? Distribusi binomial negatif adalah distribusi probabilitas yang menggambarkan jumlah percobaan Bernoulli yang diperlukan untuk [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Distribusi Binomial Negatif - Probabilitas dan Statistik<\/title>\n<meta name=\"description\" content=\"Artikel ini menjelaskan apa itu distribusi binomial negatif dan kegunaannya. 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