{"id":224,"date":"2023-08-03T23:08:41","date_gmt":"2023-08-03T23:08:41","guid":{"rendered":"https:\/\/statorials.org\/pl\/rownomierny-ciagly-rozklad\/"},"modified":"2023-08-03T23:08:41","modified_gmt":"2023-08-03T23:08:41","slug":"rownomierny-ciagly-rozklad","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/rownomierny-ciagly-rozklad\/","title":{"rendered":"R\u00f3wnomierna i ci\u0105g\u0142a dystrybucja"},"content":{"rendered":"

W tym artykule wyja\u015bniono, czym jest ci\u0105g\u0142y rozk\u0142ad r\u00f3wnomierny i do czego si\u0119 go u\u017cywa. Znajdziesz tu tak\u017ce wykres ci\u0105g\u0142ego rozk\u0142adu r\u00f3wnomiernego i w\u0142a\u015bciwo\u015bci tego typu rozk\u0142adu. <\/p>\n

<\/span> Co to jest ci\u0105g\u0142y rozk\u0142ad r\u00f3wnomierny?<\/span><\/h2>\n

Ci\u0105g\u0142y rozk\u0142ad r\u00f3wnomierny<\/strong> to rodzaj rozk\u0142adu prawdopodobie\u0144stwa, w kt\u00f3rym wszystkie warto\u015bci maj\u0105 to samo prawdopodobie\u0144stwo wyst\u0105pienia. Innymi s\u0142owy, ci\u0105g\u0142y rozk\u0142ad r\u00f3wnomierny to rozk\u0142ad, w kt\u00f3rym prawdopodobie\u0144stwo jest r\u00f3wnomiernie roz\u0142o\u017cone w pewnym przedziale.<\/p>\n

Ci\u0105g\u0142y rozk\u0142ad r\u00f3wnomierny s\u0142u\u017cy do opisu zmiennych ci\u0105g\u0142ych, kt\u00f3re maj\u0105 sta\u0142e prawdopodobie\u0144stwo. Podobnie ci\u0105g\u0142y rozk\u0142ad r\u00f3wnomierny s\u0142u\u017cy do definiowania proces\u00f3w losowych, poniewa\u017c je\u015bli wszystkie wyniki maj\u0105 to samo prawdopodobie\u0144stwo, oznacza to, \u017ce wynik jest losowy.<\/p>\n

Ci\u0105g\u0142y rozk\u0142ad r\u00f3wnomierny ma dwa charakterystyczne parametry, aib<\/em> ,<\/em> kt\u00f3re definiuj\u0105 przedzia\u0142 r\u00f3wnowa\u017cnego prawdopodobie\u0144stwa. Zatem symbolem ci\u0105g\u0142ego rozk\u0142adu r\u00f3wnomiernego jest U(a,b)<\/em> , gdzie a<\/em> i b<\/em> s\u0105 charakterystycznymi warto\u015bciami rozk\u0142adu.<\/p>\n<\/p>\n

\"X\\sim<\/p>\n<\/p>\n

Na przyk\u0142ad, je\u015bli wynik losowego eksperymentu mo\u017ce przyj\u0105\u0107 dowoln\u0105 warto\u015b\u0107 z zakresu od 5 do 9, a wszystkie mo\u017cliwe wyniki maj\u0105 to samo prawdopodobie\u0144stwo wyst\u0105pienia, eksperyment mo\u017cna symulowa\u0107 za pomoc\u0105 ci\u0105g\u0142ego r\u00f3wnomiernego rozk\u0142adu U(5,9).<\/p>\n

Ci\u0105g\u0142y rozk\u0142ad r\u00f3wnomierny nazywany jest tak\u017ce rozk\u0142adem prostok\u0105tnym<\/strong> . <\/p>\n

<\/span> Ci\u0105g\u0142a formu\u0142a rozk\u0142adu r\u00f3wnomiernego<\/span><\/h2>\n

Funkcja g\u0119sto\u015bci okre\u015blaj\u0105ca prawdopodobie\u0144stwo r\u00f3wnomiernego rozk\u0142adu to funkcja podzielona przez r\u00f3\u017cnic\u0119 mi\u0119dzy b<\/em> i a<\/em> . Zatem wz\u00f3r na ci\u0105g\u0142y rozk\u0142ad r\u00f3wnomierny<\/strong> to:<\/p>\n<\/p>\n

\"\\begin{array}{c}X\\sim<\/p>\n<\/p>\n

Natomiast skumulowan\u0105 funkcj\u0119 prawdopodobie\u0144stwa ci\u0105g\u0142ego rozk\u0142adu r\u00f3wnomiernego definiuje si\u0119 za pomoc\u0105 nast\u0119puj\u0105cego wyra\u017cenia:<\/p>\n

 *** QuickLaTeX cannot compile formula:\n\\displaystyle F(x)=\\left\\{\\begin{array}{ll}0&\\text{si }x<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id =\"grafica-de-la-distribucion-uniforme-continua\"><\/span> Graph of continuous uniform distribution<span class=\"ez-toc-section-end\"><\/span><\/h2> Since in a distribution uniform continuous probability is constant, its graphical representation is simply a function with a constant value defined in the same interval as the uniform distribution. <figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/ 08\/distribution-uniforme-continue.png\" alt=\"Continuous uniform distribution graph\" class=\"wp-image-4498\" width=\"330\" height=\"232\" srcset=\"\" sizes=\"\"><\/figure > On the other hand, the cumulative probability graph of the continuous uniform distribution is as follows: <figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-uniforme-continue-probabilite-cumulative.png\" alt=\"cumulative probability plot of a continuous uniform distribution\" class= \"wp-image-4499\" width=\"247\" height=\"193\" srcset=\"\" sizes=\"\"><\/figure><h2 class=\"wp-block-heading\"><span class=\"ez-toc -section\" id=\"caracteristicas-de-la-distribucion-uniforme-continua\"><\/span> Characteristics of the continuous uniform distribution<span class=\"ez-toc-section-end\"><\/span><\/h2 > The continuous uniform distribution has the following characteristics: <ul><li> The continuous uniform distribution is defined by two real parameters, <em>a<\/em> and <em>b<\/em>, which establish the limits in which the probability is constant.<\/li><\/ul>[latex]a,b\\in \\mathbb{R}\n\n***Error message:\nPlease use \\mathaccent for accents in math mode.\nleading text: ...continuous uniform distribution probability\nPlease use \\mathaccent for accents in math mode.\nleading text: ...if the probability is constant, its representation\nPlease use \\mathaccent for accents in math mode.\nleading text: ...a function with a constant value de\nPlease use \\mathaccent for accents in math mode.\nleading text: ...c a constant value defined in the same\nPlease use \\mathaccent for accents in math mode.\nleading text: ...On the other hand, the probability graph\nPlease use \\mathaccent for accents in math mode.\nleading text: ... part, the cumulative probability graph\nPlease use \\mathaccent for accents in math mode.\nleading text: ...nue-probabilite-cumulative.png\" alt=\"plot\n\n<\/pre>\n