Share to:

Rovnoměrné rozdělení

Rovnoměrné rozdělení pravděpodobnosti přiřazuje všem hodnotám náhodné veličiny stejnou pravděpodobnost.

Rovnoměrné rozdělení má svoji diskrétní i spojitou podobu.

Spojité rozdělení

Rovnoměrné rozdělení na intervalu $(a,b)$ , kde $-\infty <a<b<\infty$ , má ve všech bodech daného intervalu konstantní hustotu pravděpodobnosti, kterou lze vyjádřit vztahem

f(x)=\left\{{\begin{matrix}{\frac {1}{b-a}}&{\mbox{ pro }}x\in (a,b)\\0&{\mbox{ pro }}x\notin (a,b)\end{matrix}}\right.

Mimo tento daný interval je tedy hustota pravděpodobnosti nulová. Na obrázku je zobrazena hustota pravděpodobnosti rovnoměrného rozdělení.

Náhodnou veličinou s rovnoměrným rozdělením je např. chyba při zaokrouhlování.

Charakteristiky rozdělení

Střední hodnota rovnoměrného rozdělení je

\operatorname {E} (X)={\frac {a+b}{2}}

Rozptyl má hodnotu

D(X)=\sigma _{X}^{2}={\frac {{(b-a)}^{2}}{12}}

Koeficient šikmosti je nulový, tzn. $\gamma _{1}=0\,\!$ .

Koeficient špičatosti má konstantní hodnotu $\gamma _{2}=-{\frac {6}{5}}$ .

Distribuční funkce

Distribuční funkce $F(x)$ k rovnoměrnému rozdělení má tvar

F(x)=\left\{{\begin{matrix}0&{\mbox{ pro }}x\leq a\\{\frac {x-a}{b-a}}&{\mbox{ pro }}a<x<b\\1&{\mbox{ pro }}x\geq b\end{matrix}}\right.

Diskrétní rozdělení

Diskrétní rovnoměrné rozdělení popisuje náhodnou veličinu, která může nabývat $n$ hodnot se stejnou pravděpodobností ${\frac {1}{n}}$ , přičemž se předpokládá, že vzdálenosti mezi jednotlivými hodnotami náhodné veličiny jsou stejné.

Rovnoměrné rozdělení představuje nejjednodušší případ diskrétního rozdělení.

Příklad

Typickým příkladem diskrétního rovnoměrného rozdělení je hod šestistěnnou hrací kostkou, kdy pravděpodobnost padnutí každého z čísel je ${\frac {1}{6}}$ .

Související články

Rozdělení pravděpodobnosti

Externí odkazy

Obrázky, zvuky či videa k tématu rovnoměrné rozdělení na Wikimedia Commons
Online kalkulátor Rovnoměrného rozdělení

Read other articles:

Gabi Ashkenazi

Israeli politician and former military leader Gabi AshkenaziAshkenazi, in his former role of IDF chief of staff, February 2007Ministerial roles2020–2021Minister of Foreign AffairsFaction represented in the Knesset2019–2021Blue and White Personal detailsBornGabriel Ashkenazi (1954-02-25) 25 February 1954 (age 69)Hagor, IsraelResidenceKfar SabaMilitary serviceAllegiance IsraelYears of service1972–2011Rank Rav Aluf (highest rank)CommandsIDF Chief of StaffDeputy Chief of Staf...

المنطقة الفدرالية الشمالية الغربية

المنطقة الفدرالية الشمالية الغربية الإحداثيات 59°57′00″N 30°19′00″E / 59.95°N 30.316666666667°E / 59.95; 30.316666666667 [1] تاريخ التأسيس 13 مايو 2000 تقسيم إداري البلد روسيا التقسيم الأعلى روسيا العاصمة سانت بطرسبرغ خصائص جغرافية المساحة 1677900 كيلومتر مر

Chromium(II) oxide

Chromium(II) oxide Names IUPAC name chromium(II) oxide Identifiers CAS Number 12018-00-7 Y PubChem CID 3037052 CompTox Dashboard (EPA) DTXSID20152717 Properties Chemical formula CrO Molar mass 67.996 g/mol Appearance black Melting point 300 °C (572 °F; 573 K) (decomposes) Structure Crystal structure cubic, cF8 Space group Fm3m, No. 225 Except where otherwise noted, data are given for materials in their standard state (at 25 °C [77 °F], 100&...

Phantasmarana

Phantasmarana Taxonomische indeling Rijk:Animalia (Dieren)Stam:Chordata (Chordadieren)Klasse:Amfibia (Amfibieën)Orde:Anura (Kikkers)Onderorde:NeobatrachiaFamilie:Hylodidae Geslacht PhantasmaranaVittorazzi, Augusto-Alves, Neves-da-Silva, Carvalho-e-Silva, Recco-Pimentel, Toledo, Lourenço & Bruschi, 2021 Typesoort Elosia massarti[noot 1] Portaal Biologie Herpetologie Phantasmarana is een geslacht van kikkers uit de familie Hylodidae.[1] Phantasmarana werd voor...

Armed Forces Ruling Council (Nigeria)

Legal armed force council in charge during 1985 to 1993 in Nigeria Armed Forces Ruling CouncilOverviewEstablished27 August 1985 (1985-08-27)Dissolved26 August 1993 (1993-08-26)StateNigeriaLeaderChairman (Ibrahim Babangida)HeadquartersLagos Politics of Nigeria Constitution Human rights Government President (list) Bola Tinubu Vice President Kashim Shettima Cabinet Federal Parastatals Legislature National Assembly of Nigeria Senate President Godswill Akpabio (APC) D...

On Ancient Medicine

Greek medical text, c. 450–400 B.C. Hippocrates The treatise On Ancient Medicine (Greek: Περὶ Ἀρχαίας Ἰατρικῆς; Latin: De vetere medicina) is perhaps the most intriguing and compelling work of the Hippocratic Corpus. The Corpus itself is a collection of about sixty writings covering all areas of medical thought and practice. Traditionally associated with Hippocrates, (c. 460 BC – c. 370 BC) the father of Western medicine, philological evidence now suggests that it w...

Fiery-shouldered parakeet

Species of bird Fiery-shouldered parakeet Conservation status Least Concern (IUCN 3.1)[1] Scientific classification Domain: Eukaryota Kingdom: Animalia Phylum: Chordata Class: Aves Order: Psittaciformes Family: Psittacidae Genus: Pyrrhura Species: P. egregia Binomial name Pyrrhura egregia(Sclater, PL, 1881) The fiery-shouldered parakeet (Pyrrhura egregia), also known as the fiery-shouldered conure, is a species of parrot in the family Psittacidae. It is found in Brazil, Guya...

Družina, Zagorje ob Savi

Place in Upper Carniola, SloveniaDružinaDružinaLocation in SloveniaCoordinates: 46°7′13.71″N 14°58′56.18″E / 46.1204750°N 14.9822722°E / 46.1204750; 14.9822722Country SloveniaTraditional regionUpper CarniolaStatistical regionCentral SavaMunicipalityZagorje ob SaviArea • Total1.03 km2 (0.40 sq mi)Elevation448.4 m (1,471.1 ft)Population (2002) • Total7[1] Družina (pronounced [dɾuˈʒiːna&#...

رياضة فرق

رياضة فرق صنف فرعى من رياضه تعديل رياضة فرق هيا رياضه بتتلعب بين فريقين او اكتر. الرياضات الجماعيه بتعتبر من اكتر الرياضات اللى ليها شعبيه فى العالم كله. انواع العاب الفرق كتير منها كورة قدم و كورة سله والكرة الطائرة والتنس وكرة الماء واللكروس والتجديف والرجبي وا...

William Jervois

British Army general This article is about the governor. For his father, the commander of British forces in Hong Kong, see William Jervois (British Army officer). For other uses, see Jervois. Lieutenant General SirWilliam JervoisGCMG CB FRSSir William Jervois, circa 188010th Governor of the Straits SettlementsIn office8 May 1875 – 3 April 1877Preceded byAndrew ClarkeSucceeded bySir William Cleaver Francis Robinson10th Governor of South AustraliaIn office2 October 18...

Stanisław Ruziewicz

Polish mathematician Stanisław RuziewiczStanisław Ruziewicz (c.a. 1939)Born(1889-08-29)29 August 1889Kołomyja (uk. Коломия)Died12 July 1941(1941-07-12) (aged 51)Lwów (today Lviv, Ukraine), Nazi-occupied PolandNationalityPolishAlma materUniversity of LwówKnown forRuziewicz problemScientific careerFieldsMathematicsInstitutionsJan Kazimierz University, Academy of Foreign Trade in LwówDoctoral advisorWacław SierpińskiDoctoral studentsStefan Kaczmarz Stanisław Ruziew...

Christmas Eve (Kelly Clarkson song)

2017 single by Kelly Clarkson Christmas EveSingle by Kelly ClarksonReleasedNovember 30, 2017 (2017-11-30)Recorded2017Length3:00LabelAtlanticSongwriter(s) Kelly Clarkson Jason Halbert Producer(s)Jason HalbertKelly Clarkson singles chronology Love So Soft (2017) Christmas Eve (2017) I Don't Think About You (2018) Christmas Eve is a song by American singer Kelly Clarkson. Written by Clarkson with Jason Halbert, who produced it, it is a Christmas-themed song about witnessing the fe...

Devar Bhabi

1967 Pakistani filmDevar BhabiOriginal titleدیور بھابھی Directed byHassan TariqWritten byAli Sufiyan Afaqi (dialogues)Screenplay byHaasan TariqStory byArsh LakhnaviProduced bySabiha Khanum (credited as Sabiha Raza)Starring Waheed Murad Sabiha Khanum Rani Music byInayat HussainProductioncompanySantosh ProductionsRelease date 5 May 1967 (1967-05-05) CountryPakistanLanguageUrdu Devar Bhabi is a 1967 Pakistani film directed by Hassan Tariq. It is produced by Sabiha Khanum...

A.M. Hendropriyono

Netralitas artikel ini dipertanyakan. Diskusi terkait dapat dibaca pada the halaman pembicaraan. Jangan hapus pesan ini sampai kondisi untuk melakukannya terpenuhi. (Pelajari cara dan kapan saatnya untuk menghapus pesan templat ini) A.M. HendropriyonoHendropriyono pada tahun 2016Ketua Umum Partai Keadilan dan Persatuan Indonesia Ke-4Masa jabatan27 Agustus 2016 – 13 April 2018PendahuluIsran Noor (Plt.)PenggantiDiaz HendropriyonoKepala Badan Intelijen Negara Ke-11Masa jabatan...

List of mines in Zambia

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: List of mines in Zambia – news · newspapers · books · scholar · JSTOR (April 2023) (Learn how and when to remove this template message) Zambia has a large mining industry, especially in the Copperbelt region. Mopani copper and cobalt mines Main article: Mopani ...

Platanus

Genus of flowering plants constituting the family Platanaceae For the mythological figure, see Platanus (mythology). For the ancient town, see Platanus (Cilicia). For the asteroid, see 9309 Platanus. Plane tree redirects here. For the mathematical structure, see Ordered tree. PlatanusTemporal range: Late Cretaceous – Present PreꞒ Ꞓ O S D C P T J K Pg N Leaves and fruit of a London plane Scientific classification Kingdom: Plantae Clade: Tracheophytes Clade: Angiosperms Clade: Eudicots Or...

Skin of Evil

23rd episode of the 1st season of Star Trek: The Next Generation Skin of EvilStar Trek: The Next Generation episodeEpisode no.Season 1Episode 23Directed byJoseph L. ScanlanStory byJoseph StefanoTeleplay byJoseph StefanoHannah Louise ShearerFeatured musicRon JonesCinematography byEdward R. BrownProduction code122Original air dateApril 25, 1988 (1988-04-25)Guest appearances Mart McChesney as Armus Ron Gans as Voice of Armus Walker Boone as Leland T. Lynch Brad Zerbst as Nurs...

The Olsen Gang (film)

1968 film You can help expand this article with text translated from the corresponding article in Danish. (June 2023) Click [show] for important translation instructions. Machine translation, like DeepL or Google Translate, is a useful starting point for translations, but translators must revise errors as necessary and confirm that the translation is accurate, rather than simply copy-pasting machine-translated text into the English Wikipedia. Do not translate text that appears unreliable...

Bijan Kumar Mukherjea

Bijan Kumar MukherjeaKetua Hakim Mahkamah Agung IndiaMasa jabatan23 Desember 1954 – 31 Januari 1956 Informasi pribadiKebangsaanIndiaProfesiHakimSunting kotak info • L • B Bijan Kumar Mukherjea adalah hakim Mahkamah Agung India. Ia diangkat sebagai hakim di mahkamah tersebut pada tanggal 26 Januari 1950. Ia lalu terpilih sebagai Ketua Hakim Mahkamah Agung India pada tanggal 23 Desember 1954. Masa baktinya sebagai hakim di mahkamah tersebut kemudian berakhir pada tangga...

Rhône's 5th constituency

Constituency of the National Assembly of France 5th constituency of RhôneinlineConstituency of the National Assembly of FranceRhône's's 5th Constituency shown within RhôneDeputyBlandine Brocard[1]MoDemDepartmentRhôneCantonsCaluire-et-Cuire, Limonest, Neuville-sur-SaôneRegistered voters88072[2] Politics of France Political parties Elections Previous Next The 5th constituency of the Rhône (French: Cinquième circonscription du Rhône) is a French legislative constituency i...

Kembali kehalaman sebelumnya