Misali na Tambayoyin Tattaunawa Kan Rarrabawa Iri ɗaya
Rarrabawar daidaito ɗaya ce daga cikin mafi sauƙi nau'ikan rarrabawar yiwuwa a kididdiga. An raba ta zuwa manyan nau'i biyu: rarrabawar daidaito daban-daban da kuma rarrabawar daidaito mai ci gaba. A cikin wannan labarin, za mu tattauna nau'ikan rarraba daidaito guda biyu, mu ba da misalai, da kuma tattauna hanyoyin magance waɗannan matsalolin.
Rarrabawa Mai Sauƙi
Rarrabawar daidaito ta daban-daban ita ce rarraba yiwuwar da kowane sakamako na gwaji ko abin da ya faru ke da damar faruwa daidai. Misalan mafi sauƙi sune mirgina fair dice ko zaɓar kati daga saitin katunan iri ɗaya.
Misali Tambaya ta 1
Tambaya:
Diyar gaskiya tana da ɓangarori 6 masu lamba 1 zuwa 6. Kayyade yuwuwar samun 4 a kan birgima ɗaya na diyar.
Tattaunawa:
Tunda kowane gefen fair dice yana da daidaiton damar bayyana, zamu iya cewa yiwuwar kowane gefe shine:
P(A) = 1/n
Inda n shine jimlar sakamakon da zai yiwu. A wannan yanayin, n = 6.
Don haka, yuwuwar samun lamba 4 shine:
P(4) = 1/6 ≈ 0.167 ko 16.7%
Misali Tambaya ta 2
Tambaya:
Akwati yana ɗauke da ƙwallo 10 masu lamba 1 zuwa 10. Idan aka zana ƙwallon a bazata, a nemo yiwuwar cewa ƙwallon da aka zana tana da lamba fiye da 7.
Tattaunawa:
Adadin ƙwallon da suka cancanta sune ƙwallo mai lamba 8, 9, da 10. Don haka, akwai ƙwallo uku da suka cancanta daga cikin jimillar ƙwallo 10.
P(B) = adadin ƙwallo da suka cika sharuɗɗan / jimillar ƙwallo
P(B) = 3/10 = 0.3 ko 30%
Ci gaba da Rarraba Iri ɗaya
Rarrabawa iri ɗaya mai ci gaba shine rarrabawa wanda dukkan dabi'u a cikin wani tazara suna da daidaiton yuwuwar faruwa. Wannan rarrabawa sau da yawa yakan taso ne a yanayi inda kowane sakamako a cikin wani iyaka yake da yuwuwar daidai.
Misali Tambaya ta 3
Tambaya:
A ce X wani canji ne na bazuwar da aka rarraba daidai gwargwado tsakanin 0 da 1. Nemo yuwuwar cewa X yana tsakanin 0.25 da 0.75.
Tattaunawa:
Don ci gaba da rarrabawa iri ɗaya, yawan yuwuwar yana nan a duk tsawon lokacin. A wannan yanayin, tazara tana daga 0 zuwa 1, wanda ke nufin yawan yuwuwar (f(x)) shine 1 saboda rarraba iri ɗaya dole ne ya sami jimillar yanki a ƙarƙashin lanƙwasa na 1.
Ana iya ƙididdige yiwuwar cewa X yana tsakanin 0.25 da 0.75 a matsayin yanki da ke ƙarƙashin PDF (Probability Density Function) tsakanin waɗannan iyakoki guda biyu.
P(0.25 ≤ X ≤ 0.75) = (b – a) / (d – c)
Inda a da b su ne ƙananan da manyan iyakoki na tazara da muke nema, kuma c da d su ne iyakokin rarrabawa iri ɗaya. A wannan yanayin, a = 0.25, b = 0.75, c = 0, da d = 1.
P(0.25 ≤
Don haka, yuwuwar cewa X yana tsakanin 0.25 da 0.75 shine 0.5 ko 50%.
Misali Tambaya ta 4
Tambaya:
Ana yin ma'auni da kayan aiki mai rarraba daidaito iri ɗaya a tsawon tazara [2, 5]. Nemo yuwuwar cewa ma'aunin yana samar da ƙima tsakanin 3 da 4.
Tattaunawa:
Don rarrabawa iri ɗaya a kan tazara [2, 5], yawan yuwuwar yana dawwama kuma jimlar yankin da ke ƙarƙashin lanƙwasa shine 1. Don haka, yawan yuwuwar (f(x)) shine 1/(5-2) = 1/3.
Yiwuwar cewa ma'aunin yana tsakanin 3 da 4 shine:
P(3 ≤ X ≤ 4) = (b – a) / (d – c)
Inda a da b su ne iyakokin tazara da muke nema, kuma c da d su ne iyakokin rarrabawa iri ɗaya. A wannan yanayin, a = 3, b = 4, c = 2, da d = 5.
P(3 ≤ X ≤ 4) = (4 – 3) / (5 – 2) = 1/3 ≈ 0.333 ko 33.3%
Kammalawa
Rarrabawar daidaito kayan aiki ne mai matuƙar amfani a cikin nazarin yiwuwar da ƙididdiga saboda sauƙin fahimta da sauƙin fahimta. A cikin siffofi daban-daban da kuma masu ci gaba, rarraba daidaito yana tabbatar da cewa kowane sakamako a cikin wani yanki yana da irin wannan yuwuwar.
Mabuɗin Maɓalli
1. Rarraba Daidaito: Yiwuwar kowane sakamako a cikin wani takamaiman kewayon iri ɗaya ne. Misali: jefar da fair diam.
2. Ci gaba da Rarraba Daidaito: Yawan yuwuwar yana nan a duk tsawon lokacin. Misali: auna tsayi ko nauyi ta amfani da kayan aiki mai inganci a cikin wani takamaiman iyaka.
Ta hanyar fahimtar wannan ra'ayi da kuma ta hanyar misalai da tattaunawa, za mu iya amfani da rarrabawar iri ɗaya ga yanayi da bincike daban-daban na zahiri cikin sauƙi. Wannan yana taimakawa wajen fayyace abubuwan da ke da sakamako iri ɗaya, ko a cikin tsari daban-daban ko kuma a ci gaba.
Rarrabawa iri ɗaya suna da amfani ba kawai a cikin kididdiga ba, har ma a cikin kimiyyar kwamfuta, injiniyanci, tattalin arziki, da sauran fannoni da yawa inda ake buƙatar yanke shawara ko nazarin bayanai. Misali, a cikin kwaikwayon Monte Carlo, ana amfani da rarrabawa iri ɗaya don samar da vectors bazuwar a cikin takamaiman kewayon, wanda daga nan ake amfani da shi don kimanta yanayi da sakamako daban-daban.
Muna fatan wannan labarin ya taimaka muku fahimtar rarrabawa iri ɗaya da kuma yadda ake magance matsaloli da shi. Ku ci gaba da yin aiki don ƙwarewa a wannan ra'ayi da kuma amfani da shi ga al'amuran da suka shafi fagen ku.
