{"id":2874,"date":"2024-10-24T17:00:03","date_gmt":"2024-10-24T15:00:03","guid":{"rendered":"https:\/\/ellistat.com\/?post_type=ressource-pedagogiqu&#038;p=2874"},"modified":"2024-10-24T17:01:21","modified_gmt":"2024-10-24T15:01:21","slug":"hipergometrias-torveny","status":"publish","type":"ressource-pedagogiqu","link":"https:\/\/ellistat.com\/hu\/ressource-pedagogiqu\/loi-hypergeometrique\/","title":{"rendered":"Hipergeometriai t\u00f6rv\u00e9ny"},"content":{"rendered":"<p>A hipergeometriai eloszl\u00e1s egy diszkr\u00e9t val\u00f3sz\u00edn\u0171s\u00e9gi eloszl\u00e1s, amely a sikerek sz\u00e1m\u00e1t modellezi egy meghat\u00e1rozott sz\u00e1m\u00fa sikeres \u00e9s sikertelen objektumot tartalmaz\u00f3 v\u00e9ges popul\u00e1ci\u00f3b\u00f3l p\u00f3tl\u00e1s n\u00e9lk\u00fcl vett, r\u00f6gz\u00edtett m\u00e9ret\u0171 mint\u00e1ban. Gyakran haszn\u00e1lj\u00e1k olyan helyzetek modellez\u00e9s\u00e9re, ahol a szelekci\u00f3 nem f\u00fcggetlen, mivel minden egyes h\u00faz\u00e1s befoly\u00e1solja a popul\u00e1ci\u00f3 \u00f6sszet\u00e9tel\u00e9t.&nbsp;<\/p>\n\n\n\n<p>\u00cdme a hipergeometriai t\u00f6rv\u00e9ny legfontosabb jellemz\u0151i:&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>V\u00e9ges popul\u00e1ci\u00f3<\/strong> A teljes popul\u00e1ci\u00f3 meghat\u00e1rozott sz\u00e1m\u00fa t\u00e1rgyat tartalmaz, p\u00e9ld\u00e1ul k\u00e1rty\u00e1kat, goly\u00f3kat, \u00e9rm\u00e9ket stb.&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>A siker \u00e9s a kudarc t\u00e1rgyai<\/strong> A popul\u00e1ci\u00f3 k\u00e9t csoportra oszlik: sikerobjektumok (pl. megjel\u00f6lt k\u00e1rty\u00e1k, nyertes goly\u00f3k) \u00e9s kudarcobjektumok (pl. nem megjel\u00f6lt k\u00e1rty\u00e1k, vesztes goly\u00f3k).&nbsp;<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Rajzol\u00e1s csere n\u00e9lk\u00fcl<\/strong> A mint\u00e1t \u00fagy sorsoljuk ki, hogy a t\u00e1rgyakat minden egyes sorsol\u00e1s ut\u00e1n nem visszaadjuk a popul\u00e1ci\u00f3nak. Ez azt jelenti, hogy egy t\u00e1rgy kih\u00faz\u00e1s\u00e1nak val\u00f3sz\u00edn\u0171s\u00e9ge minden egyes h\u00faz\u00e1s ut\u00e1n v\u00e1ltozik.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p>A hipergeometriai eloszl\u00e1s val\u00f3sz\u00edn\u0171s\u00e9gi t\u00f6megf\u00fcggv\u00e9ny\u00e9t (PMF) a k\u00f6vetkez\u0151 k\u00e9plet adja meg:&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\ud835\udc43(\ud835\udc4b=\ud835\udc58)=\ud835\udc36\ud835\udc3e\ud835\udc58\u2217\ud835\udc36\ud835\udc41-\ud835\udc3e\ud835\udc5b-\ud835\udc58\ud835\udc36\ud835\udc41\ud835\udc5bPX=k=CkK\u2217Cn-kN-KCnN<\/span><\/p>\n\n\n\n<p>ahol :&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>N a teljes popul\u00e1ci\u00f3 m\u00e9rete,\u00a0<\/li>\n\n\n\n<li>K a sikeres objektumok sz\u00e1ma a popul\u00e1ci\u00f3ban,\u00a0<\/li>\n\n\n\n<li>n a minta m\u00e9rete,\u00a0<\/li>\n\n\n\n<li>k a mint\u00e1ban szerepl\u0151 sikerek sz\u00e1ma,\u00a0<\/li>\n<\/ul>\n\n\n\n<p>A hipergeometriai eloszl\u00e1s \u00e1tlaga (v\u00e1rakoz\u00e1sa) :<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\mu=n*\\frac{K}{N}<\/span><\/p>\n\n\n\n<p>A binomi\u00e1lis eloszl\u00e1s sz\u00f3r\u00e1sa :<\/p>\n\n\n\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\sigma=n<em>\\frac{K<\/em>(N-K)*(N-n)}{N^{2}(N-1)}<\/span><\/p>\n\n\n\n<p>A hipergeometriai t\u00f6rv\u00e9nyt sz\u00e1mos ter\u00fcleten haszn\u00e1lj\u00e1k, p\u00e9ld\u00e1ul a statisztik\u00e1ban, a genetik\u00e1ban, a k\u00f6zgazdas\u00e1gtanban \u00e9s m\u00e1s olyan ter\u00fcleteken, ahol a mint\u00e1kat csere n\u00e9lk\u00fcl h\u00fazz\u00e1k ki egy v\u00e9ges sokas\u00e1gb\u00f3l. Abban k\u00fcl\u00f6nb\u00f6zik a binomi\u00e1lis eloszl\u00e1st\u00f3l, hogy figyelembe veszi a siker val\u00f3sz\u00edn\u0171s\u00e9g\u00e9nek v\u00e1ltoz\u00e1s\u00e1t minden egyes h\u00faz\u00e1sn\u00e1l.&nbsp;<\/p>","protected":false},"featured_media":0,"template":"","meta":{"_acf_changed":false},"menu-ressource-pedagogique":[],"class_list":["post-2874","ressource-pedagogiqu","type-ressource-pedagogiqu","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Loi Hyperg\u00e9om\u00e9trique - Ellistat<\/title>\n<meta name=\"description\" content=\"La loi hyperg\u00e9om\u00e9trique est souvent utilis\u00e9e pour mod\u00e9liser des situations o\u00f9 la s\u00e9lection n&#039;est pas ind\u00e9pendante.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ellistat.com\/hu\/oktatasi-forras\/hipergometrias-torveny\/\" \/>\n<meta property=\"og:locale\" content=\"hu_HU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Loi Hyperg\u00e9om\u00e9trique - 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