{"id":2009,"date":"2023-07-24T02:36:15","date_gmt":"2023-07-24T02:36:15","guid":{"rendered":"https:\/\/statorials.org\/pl\/wartosc-oczekiwana-w-r\/"},"modified":"2023-07-24T02:36:15","modified_gmt":"2023-07-24T02:36:15","slug":"wartosc-oczekiwana-w-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/wartosc-oczekiwana-w-r\/","title":{"rendered":"Jak obliczy\u0107 oczekiwan\u0105 warto\u015b\u0107 w r (z przyk\u0142adami)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Rozk\u0142ad prawdopodobie\u0144stwa m\u00f3wi nam, jakie jest prawdopodobie\u0144stwo, \u017ce <a href=\"https:\/\/statorials.org\/pl\/zmienne-losowe\/\" target=\"_blank\" rel=\"noopener\">zmienna losowa<\/a> przyjmie okre\u015blone warto\u015bci.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Na przyk\u0142ad poni\u017cszy rozk\u0142ad prawdopodobie\u0144stwa informuje nas o prawdopodobie\u0144stwie, \u017ce dana dru\u017cyna pi\u0142karska zdob\u0119dzie okre\u015blon\u0105 liczb\u0119 bramek w danym meczu:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-14093 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/moyennedist1.png\" alt=\"\" width=\"261\" height=\"185\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Aby znale\u017a\u0107 <strong>warto\u015b\u0107 oczekiwan\u0105<\/strong> rozk\u0142adu prawdopodobie\u0144stwa, mo\u017cemy skorzysta\u0107 z nast\u0119puj\u0105cego wzoru:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00b5 = \u03a3x * P(x)<\/span><\/p>\n<p> <span style=\"color: #000000;\">Z\u0142oto:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">x: warto\u015b\u0107 danych<\/span><\/li>\n<li> <span style=\"color: #000000;\">P(x): Prawdopodobie\u0144stwo warto\u015bci<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Na przyk\u0142ad oczekiwan\u0105 liczb\u0119 bramek dla dru\u017cyny pi\u0142karskiej mo\u017cna obliczy\u0107 w nast\u0119puj\u0105cy spos\u00f3b:<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u03bc = 0*0,18 + 1*0,34 + 2*0,35 + 3*0,11 + 4*0,02 = <strong>1,45<\/strong> gola.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Aby obliczy\u0107 warto\u015b\u0107 oczekiwan\u0105 rozk\u0142adu prawdopodobie\u0144stwa w R, mo\u017cemy skorzysta\u0107 z jednej z trzech metod:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#method 1<\/span>\nsum(vals*probs)\n\n<span style=\"color: #008080;\">#method 2\n<\/span>weighted. <span style=\"color: #3366ff;\">mean<\/span> (vals, probs)\n\n<span style=\"color: #008080;\">#method 3\n<\/span>c(vals <span style=\"color: #800080;\">%*%<\/span> probs)\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Wszystkie trzy metody zwr\u00f3c\u0105 ten sam wynik.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poni\u017csze przyk\u0142ady pokazuj\u0105, jak u\u017cywa\u0107 ka\u017cdej z tych metod w R.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 1: Oczekiwana warto\u015b\u0107 przy u\u017cyciu sum()<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak obliczy\u0107 warto\u015b\u0107 oczekiwan\u0105 rozk\u0142adu prawdopodobie\u0144stwa za pomoc\u0105 funkcji <strong>sum()<\/strong> :<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define values\n<span style=\"color: #000000;\">vals &lt;- c(0, 1, 2, 3, 4)\n<\/span>\n#define probabilities\n<span style=\"color: #000000;\">probs &lt;- c(.18, .34, .35, .11, .02)\n<\/span>\n#calculate expected value<\/span>\nsum(vals*probs)\n\n[1] 1.45\n<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 2:<\/strong><\/span> <span style=\"color: #000000;\"><strong>Warto\u015b\u0107 oczekiwana przy u\u017cyciu metody Weighted.mean()<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak obliczy\u0107 warto\u015b\u0107 oczekiwan\u0105 rozk\u0142adu prawdopodobie\u0144stwa przy u\u017cyciu wbudowanej funkcji inweighted.mean <strong>()<\/strong> w R:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define values\n<span style=\"color: #000000;\">vals &lt;- c(0, 1, 2, 3, 4)\n<\/span>\n#define probabilities\n<span style=\"color: #000000;\">probs &lt;- c(.18, .34, .35, .11, .02)\n<\/span>\n#calculate expected value<\/span>\nweighted. <span style=\"color: #3366ff;\">mean<\/span> (vals, probs)\n\n[1] 1.45<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 3: Warto\u015b\u0107 oczekiwana przy u\u017cyciu c()<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak obliczy\u0107 warto\u015b\u0107 oczekiwan\u0105 rozk\u0142adu prawdopodobie\u0144stwa za pomoc\u0105 wbudowanej funkcji <strong>c()<\/strong> w R:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define values\n<span style=\"color: #000000;\">vals &lt;- c(0, 1, 2, 3, 4)\n<\/span>\n#define probabilities\n<span style=\"color: #000000;\">probs &lt;- c(.18, .34, .35, .11, .02)\n<\/span>\n#calculate expected value<\/span>\nc(vals <span style=\"color: #800080;\">%*%<\/span> probs)\n\n[1] 1.45<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Nale\u017cy zauwa\u017cy\u0107, \u017ce wszystkie trzy metody zwr\u00f3ci\u0142y t\u0119 sam\u0105 oczekiwan\u0105 warto\u015b\u0107.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/pl\/funkcja-srednia-w-r\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 \u015bredni\u0105 w R<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/srednia-geometryczna-w-r\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 \u015bredni\u0105 geometryczn\u0105 w R<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/srednia-wazona-w-r\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 \u015bredni\u0105 wa\u017con\u0105 w R<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Rozk\u0142ad prawdopodobie\u0144stwa m\u00f3wi nam, jakie jest prawdopodobie\u0144stwo, \u017ce zmienna losowa przyjmie okre\u015blone warto\u015bci. Na przyk\u0142ad poni\u017cszy rozk\u0142ad prawdopodobie\u0144stwa informuje nas o prawdopodobie\u0144stwie, \u017ce dana dru\u017cyna pi\u0142karska zdob\u0119dzie okre\u015blon\u0105 liczb\u0119 bramek w danym meczu: Aby znale\u017a\u0107 warto\u015b\u0107 oczekiwan\u0105 rozk\u0142adu prawdopodobie\u0144stwa, mo\u017cemy skorzysta\u0107 z nast\u0119puj\u0105cego wzoru: \u00b5 = \u03a3x * P(x) Z\u0142oto: x: warto\u015b\u0107 danych P(x): Prawdopodobie\u0144stwo [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-2009","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Jak obliczy\u0107 warto\u015b\u0107 oczekiwan\u0105 w R (z przyk\u0142adami) - 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