{"id":3934,"date":"2023-07-14T16:10:59","date_gmt":"2023-07-14T16:10:59","guid":{"rendered":"https:\/\/statorials.org\/id\/nilai-yang-diharapkan-x2\/"},"modified":"2023-07-14T16:10:59","modified_gmt":"2023-07-14T16:10:59","slug":"nilai-yang-diharapkan-x2","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/nilai-yang-diharapkan-x2\/","title":{"rendered":"Cara menghitung nilai yang diharapkan dari x^2"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Untuk variabel acak yang dilambangkan dengan X, Anda dapat menggunakan rumus berikut untuk menghitung nilai yang diharapkan dari X <sup>2<\/sup> :<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>E(X <sup>2<\/sup> ) = \u03a3x <sup>2<\/sup> * p(x)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Emas:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u03a3<\/strong> : Simbol yang berarti \u201cjumlah\u201d<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>x<\/strong> : Nilai variabel acak<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p(x)<\/strong> : Probabilitas bahwa variabel acak mengambil nilai tertentu<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Contoh berikut menunjukkan cara menggunakan rumus ini dalam praktik.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Contoh: Perhitungan nilai yang diharapkan dari X <sup>2<\/sup><\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Misalkan kita mempunyai tabel distribusi probabilitas berikut yang menggambarkan probabilitas suatu variabel acak,<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-31621 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/x2_1.jpg\" alt=\"\" width=\"266\" height=\"253\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">Untuk menghitung nilai yang diharapkan dari X <sup>2<\/sup> , kita dapat menggunakan rumus berikut:<\/span><\/p>\n<p> <span style=\"color: #000000;\">E(X <sup>2<\/sup> ) = \u03a3x <sup>2<\/sup> * p(x)<\/span><\/p>\n<p> <span style=\"color: #000000;\">E(X <sup>2<\/sup> ) = (0) <sup>2<\/sup> *.06 + (1) <sup>2<\/sup> *.15 + (2) <sup>2<\/sup> *.17 + (3) <sup>2<\/sup> *.24 + (4) <sup>2<\/sup> *.23 + (5) <sup>2<\/sup> *.09 + (6) <sup>2<\/sup> *.06<\/span><\/p>\n<p> <span style=\"color: #000000;\">E(X <sup>2<\/sup> ) = 0 + 0,15 + 0,68 + 2,16 + 3,68 + 2,25+ 2,16<\/span><\/p>\n<p> <span style=\"color: #000000;\">E( <sup>X2<\/sup> ) = 11,08<\/span><\/p>\n<p> <span style=\"color: #000000;\">Nilai yang diharapkan dari X <sup>2<\/sup> adalah <strong>11.08<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Perhatikan bahwa variabel acak ini adalah <strong>variabel acak diskrit<\/strong> , artinya variabel tersebut hanya dapat mengambil sejumlah nilai yang terbatas.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Jika X adalah <strong>variabel acak kontinu<\/strong> , kita harus menggunakan rumus berikut untuk menghitung nilai yang diharapkan dari X <sup>2<\/sup> :<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">E(X <sup>2<\/sup> ) = \u222b x <sup>2<\/sup> f(x)dx<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">Emas:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u222b: Simbol yang berarti \u201cintegrasi\u201d<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>f(x)<\/strong> : <a href=\"https:\/\/statorials.org\/id\/cdf-vs-pdf\/\" target=\"_blank\" rel=\"noopener\">Pdf<\/a> berlanjut untuk variabel acak<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Saat menghitung nilai ekspektasi <sup>X2<\/sup> untuk variabel acak kontinu, kami biasanya menggunakan perangkat lunak statistik karena penghitungan ini lebih sulit dilakukan secara manual.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Sumber daya tambahan<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Tutorial berikut menjelaskan cara melakukan tugas umum lainnya dalam statistik:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/id\/rata-rata-distribusi-probabilitas\/\" target=\"_blank\" rel=\"noopener\">Bagaimana mencari mean dari distribusi probabilitas<\/a><br \/> <a href=\"https:\/\/statorials.org\/id\/deviasi-standar-dari-distribusi-probabilitas\/\" target=\"_blank\" rel=\"noopener\">Bagaimana mencari simpangan baku dari suatu distribusi probabilitas<\/a><br \/> <a href=\"https:\/\/statorials.org\/id\/varians-dari-distribusi-probabilitas\/\" target=\"_blank\" rel=\"noopener\">Bagaimana menemukan varians dari distribusi probabilitas<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Untuk variabel acak yang dilambangkan dengan X, Anda dapat menggunakan rumus berikut untuk menghitung nilai yang diharapkan dari X 2 : E(X 2 ) = \u03a3x 2 * p(x) Emas: \u03a3 : Simbol yang berarti \u201cjumlah\u201d x : Nilai variabel acak p(x) : Probabilitas bahwa variabel acak mengambil nilai tertentu Contoh berikut menunjukkan cara menggunakan [&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>Cara menghitung nilai yang diharapkan dari X^2 \u2013 Statologi<\/title>\n<meta name=\"description\" content=\"Tutorial ini menjelaskan cara menghitung nilai yang diharapkan dari X^2, dengan 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\/nilai-yang-diharapkan-x2\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Cara menghitung nilai yang diharapkan dari X^2 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