Nezimaphambili ezingundoqo mbono lilonke. Imithetho mbono kungenzeka

Abantu abaninzi, xa ujongene lengcinga 'theory amathuba ", watyhwatyhwa, ndicinga ukuba into obungathethekiyo, kunzima kakhulu. Kodwa ke okunene kabuhlungu kangaka. Namhlanje sijonga nezimaphambili ezingundoqo kwethiyori ngokuqinisekileyo, funda ukucombulula iingxaki yimizekelo eziphathekayo.

isayensi

Yintoni ukufunda kwisebe imathematika njenge "ithiyori namathuba '? Uphawula indlela iziganeko random kunye variables. Ngokuba lixesha lokuqala umba Wezazinzulu ngenkulungwane elinesibhozo, xa efunda ukungcakaza. nezimaphambili ezingundoqo mbono lilonke - siganeko. Yinto nayiphi na into yokuba kuchazwe ngamava okanye okuboniweyo. Kodwa yintoni na amava? Enye ngcamango e-worldwork theory lilonke. Oku kuthetha ukuba le nxalenye iimeko ngempazamo, yaye kunye nenjongo. Ngokuphathelele ngohlolo, kukho umphandi akenzi inxaxheba amava, kodwa ingqina kwezi ziganeko, lungenasiphumo ngokuqhubekayo.

izenzakalo

Siye safumanisa ukuba le ngcamango ngobhalo okuba - lo mcimbi, kodwa akazange acinge yokuhlela. Bonke bephela yahlulwe kwezi ndidi zilandelayo:

• Ezinokuthenjwa.
• Ayinakwenzeka.
• Random.

Kungakhathaliseki ukuba yintoni na umcimbi, nto nje wabona okanye idalwe ngexesha le yomzamo, ukuba azichaphazeleki koku yokuhlela. Sinikezela zonke uhlobo ukuhlangana ngokwahlukeneyo.

isiganeko esithile

Le yinyaniso apho ukwenza iseti eyimfuneko imisebenzi. Ukuze siqonde ngcono le uqobo, kungcono ukunika imizekelo embalwa. Oku ilawulwe umthetho physics, chemistry, ezoqoqosho, kunye nezibalo eziphezulu. theory amathuba iquka ingqiqo ezibalulekileyo ezifana ngesiganeko esibalulekileyo. Nantsi eminye imizekelo:

• ukusebenza kwaye ufumane umvuzo ngohlobo umvuzo.
• Well baphumelela iimviwo, wegqitha ukhuphiswano ukuze ukufumana umvuzo ngohlobo zokwamkelwa kwiziko lemfundo.
• Siye imali ebhankini, ukuyibuyisela xa kuyimfuneko.

iziganeko ezinjalo ziyinyaniso. Ukuba siye sazaliseka zonke iimeko eziyimfuneko, qiniseka ukuba ufumane isiphumo kulindeleke.

umcimbi akunakwenzeka

Ngoku sicinga iziqalelo ngobhalo lilonke. Sinikezela ukuya kucaciswa kwezi ndidi zilandelayo zeziganeko - ezizezi engenakwenzeka. Ukuqalisa uchaze ulawulo ibalulekileyo - amathuba isiganeko engenakwenzeka ngu zero.

Ukusuka ngcamango akakwazi derogated ekucombululeni iingxaki. Ukuze ubone imizekelo iziganeko ezinjalo:

• Amanzi emkhenkceni obushushu plus ezilishumi (akunakwenzeka).
• Ukungabikho umbane aluchaphazeli imveliso (njengoko ayinakwenzeka njengoko bekunjalo kumzekelo wokuqala).

imizekelo ezininzi zinikwa ayikho kuyimfuneko, njengoko kuchaziwe ngentla kakhulu ngokucacileyo ibonisa undoqo kolu didi. isiganeko akunakwenzeka akwenzeki phakathi nokuhlola naphantsi kwazo naziphi na iimeko.

izenzakalo Random

Ngokufundisisa iziqalo theory ngokuqinisekileyo, ingqalelo ekhethekileyo kufuneka ihlawulwe uhlobo elinikiweyo lomsitho. Aba ngabo befunda le inzululwazi. Ngenxa kumava into kunokwenzeka okanye hayi. Ukongeza, uvavanyo inani mda amaxesha ekuLunyukisiweyo ngazo zinakho ukuqhutywa. imizekelo ziquka:

• Aphosa lwemali - yinto amava, okanye uvavanyo, ukulahlekelwa njengokhozi - esi siganeko.
• Ngokuyihlutha ibhola evela engxoweni ungaveli - test, ubanjwe ibhola red - esi siganeko kunye njalo njalo.

Imizekelo enjalo ingaba i esingenakubalwa, kodwa, ngokubanzi, kufuneka ziqondwe. Ukushwankathela kunye nokumisa i-ulwazi malunga neziganeko itafile. izifundo theory okuba kuphela uhlobo yokugqibela thaca bonke.

imithetho

Kwenzeke theory - isayensi lifunda ithuba ilahleko yaso nasiphi na isiganeko. Njengabantu abanye, iye eminye imithetho. Le mithetho elandelayo theory kwenzeke:

• Ukuhlangabezana ulandelelwano variables random.
• Umthetho amanani amakhulu.

Xa kubalwa amathuba amaqela zingasetyenziswa iziganeko ezintsonkothileyo kulula ukuwaphumeza iziphumo lula yaye ngokukhawuleza indlela. Kufuneka kuqatshelwe ukuba imithetho theory linokuba kube lula onokuyibonisa ngoncedo ezinye theorems. Sicebisa ukuba uqale aqhelane umthetho wokuqala.

Ukuhlangabezana ulandelelwano variables random

Qaphela ukuba ukuhlangabezana lweentlobo ezininzi:

• Ulandelelwano eziguquguqukayo random ukuhlangabezana lilonke.
• Phantse engenakwenzeka.
• RMS convergence.
• Ukuhlangabezana kwi GhostScript.

Ngoko ke, kubhabho, kunzima kakhulu ukuba uliqonde kakuhle. Nazi iinkcazelo eza kunceda ukuqonda nesihloko. Okokuqala look lokuqala. Ulandelelwano kuthiwa ukuhlangabezana ngokuqinisekileyo, ukuba le meko zilandelayo: n osondela Infinity, inani wafuna yi kulandelelwano mkhulu zero kufutshane yunithi.

Yiya imboniselo elilandelayo, phantse ngokuqinisekileyo. Bathi kulandelelwano converges phantse ngokuqinisekileyo ukuba variable random kunye n othambekele infinity, kunye R, ukulima ixabiso kufutshane umanyano.

Uhlobo elandelayo - kukuhlangana RMS. Xa usebenzisa ukuhlangabezana SC-learning lweenkqubo random kumda wesangqa kunciphisa ekufundweni iinkqubo random nokulawula.

Ngaba uhlobo yokugqibela, makhe sijonge ngokufutshane yaye ukuya ngqo ngesisombululo iingxaki. Ukuhlangabezana unikezelo inomnye igama - "amandla", uze uchaze ukuba kutheni. Kuhlangana buthathaka - na ukuhlangabezana imisebenzi ukuhanjiswa kuzo zonke iingongoma yokuqhubekeka nomsebenzi lonikezelo umda.

Qiniseka ukugcina sithembiso: ukuhlangabezana zithokombisile yahlukile zonke ngasentla ukuba ejikelezayo Womendo abakacaci kwi isithuba namathuba. Oku kuyenzeka kuba i imeko akhiwe kuphela besebenzisa imisebenzi zokusasaza.

Umthetho amanani amakhulu

ngumncedi mkhulu ubungqina bawo umthetho abaya kuba theorems ithiyori ngokuqinisekileyo, ezifana:

• ukungalingani Chebyshev.
• theorem Chebyshev kaThixo.
• Ngokubanzi Chebyshev theorem.
• Markov theorem.

Ukuba ingqalelo zonke ezi theorems, ngoko umba ingathatha amashumi ezininzi kweemakhishithi. Thina umsebenzi ophambili - na isicelo kwethiyori lilonke in practice. Sinikezela ngoku wena wenze oko. Kodwa ngaphambi kokuba siqwalasele elikuwo theory ngokuqinisekileyo, ukuba amaqabane ezingundoqo ekusombululeni iingxaki.

elikuwo

Ukususela yokuqala, siye sele sibonile, xa sithetha umcimbi engenakwenzeka. Makhe khumbula: amathuba isiganeko engenakwenzeka ngu zero. Umzekelo we wanikela ecacileyo kakhulu siwakhumbula: ikhephu wawa i lobushushu air degrees amathathu Celsius.

Eyesibini ngolu hlobo lulandelayo: isiganeko esithile kwenzeka kunye umanyano lilonke. Ngoku siza kubonisa kubhaliwe kwathiwa njani na ngoncedo ulwimi lweMathematika: P (B) = 1.

Okwesithathu: A isiganeko random kwenzeka okanye hayi, kodwa ithuba lihlala ziyahluka ukusuka kwiqanda ukuya kwenye. Ukusondela ukuba kumanyano, amathuba angaphezulu; ukuba ixabiso kufutshane zero, amathuba iphantsi kakhulu. Sibhala le ulwimi lweMathematika: 0

Cinga yokugqibela, saziwe yesine, oko kukuthi: umdibaniso amathuba iziganeko ezibini ilingana isamba ebezinokwenzeka zabo. Bhala amagama zezibalo: P (A + B) = P (A) + P (B).

Elikuwo theory amathuba - oku umthetho elula engayi kuba nzima ukukhumbula. Makhe uzame ukusombulula iingxaki ezithile, ngokusekelwe kulwazi kakade.

itikiti leloto

Okokuqala, cinga nje ngomzekelo elula - lelotho. Khawucinge ukuba uthenge itikiti leloto ngenxa amathamsanqa. Yintoni na amathuba ukuba uza kuphumelela engange ubuncinane amabini? ngenani lilonke ubandakanyeke iwaka amatikiti, omnye olo ibhaso engange ezimakhulu mahlanu, engange neshumi, engange mabini anamanci mahlanu, nekhulu - amahlanu. Umsebenzi thiyori amathuba ngokusekelwe yokufumana njani indlela eya luck. Ngoku kunye sihlalutya isigqibo ngaphezu kwimboniselo Tasks.

Ukuba abonisa yi Ibhaso engange ezimakhulu mahlanu, ngoko amathuba A ulingana 0.001. Sazi njani? Kufuneka nje inani lamatikiti "Lucky" lahlulwe ngenani lilonke (kulo mzekelo: 1/1000).

In - Kukho mntu ikhulu engange, linokuba iya kulingana ukuya 0,01. Ngoku senzé ngendlela efanayo njengoko intshukumo yokugqibela (10/1000)

C - kunomvuzo engange mabini. Fumana ngokuqinisekileyo, loo nto ilingana 0.05.

Ezinye amatikiti abanamdla thina, njengoko imali yabo umvuzo ngaphantsi kwe kucacisiwe kule meko. Faka i saziwe sesine: Amathuba emagqabini engange ubuncinane amabini yi P (A) + P (B) + P (C). Le P ncwadi ibonisa amathuba imvelaphi isiganeko, sibe amanyathelo odlulileyo sele wabafumana. Kuhleli kuphela walala phantsi idata kuyimfuneko, impendulo sifumana 0,061. Eli nani liya kuba impendulo yombuzo emisebenzi.

sinendawo of Cards

Iingxaki kwithiyori ngokuqinisekileyo, kukho kwakhona anzima, umzekelo, ukuthatha umsebenzi olandelayo. Phambi kokuba sinendawo of amakhadi ezingamashumi amathathu anesithandathu. umsebenzi wakho - ukuzoba amakhadi ezimbini zilandelelana, ngaphandle okuxuba mfumba, amakhadi yokuqala neyesibini kufuneka Aces, iisuti musa akunamsebenzi.

Okokuqala, fumana amathuba ukuba ikhadi wokuqala i-ACE, le yantlukwano amane anamanci mathathu anesithandathu. Sibeke ngakuwe. Sifumana ikhadi yesibini i-ACE kunye amathuba yayingamakhulu amathathu amawaka amathathu yesihlanu. Amathuba isiganeko yesibini ixhomekeke apho ikhadi sasuka eyokuqala, sinomdla kuzo, yayi-ACE okanye hayi. Kulo kulandela ukuba xa kuthe kuxhomekeke umcimbi A.

Inyathelo elilandelayo sifumana amathuba ukuphunyezwa ngaxeshanye, okt, nande A no B. Umsebenzi wabo ngolu hlobo lulandelayo: amathuba isiganeko omnye liphindaphindwe amathuba yoxhomekeko esinye, thina ukubala, sigqibe ukuba isiganeko yokuqala eyenzekile, oko kukuthi, ikhadi yokuqala sasuka i-ACE.

Ukuze abe wonke icacile, anike ukwalatha element njengoko amathuba olunemiqathango lwe esi siganeko. Oku kubalwa kucingelwa ukuba siganeko A kwenzeke. Oku kubalwa ngale ndlela ilandelayo: P (B / A).

Thina yandisa isisombululo kwingxaki wethu: P (A _* B) = P (A) _* P (B / A) okanye P (A _* B) = P (B) _* P (A / B). Linokuba yi _{(4/36) * ((3/35)} / (4/36) ibalwa ngokusondeza ukuya ngokwekhulu ekufutshane Thina: .. _{0,11 * (0,09 / 0,11) =} 0,11 * 0 , 82 = 0.09. Amathuba ukuba ndirhole Aces ezimbini emgceni ulingana hundredths ezisithoba. ixabiso incinane kakhulu, kulandela ukuba ngenene ingenzeka isiganeko lisezantsi kakhulu.

igumbi ukhohliwe

Sinikezela ukwenza ezinye iinketho ezininzi kwemisebenzi lifunda le ngcamango lilonke. Imizekelo izisombululo yezinye yabo ubone kweli nqaku, zama ukusombulula le ngxaki zilandelayo: Le nkwenkwe azilibale inombolo yefowuni ukuba umvo yokugqibela nomhlobo wakhe, kodwa ukususela ubizo kwakubalulekile kakhulu, ngoko waqalisa ngamnye abuthe ke. Kufuneka ukuba ukubala amathuba ukuba wothini na ukuzibiza, akukho ngaphezu kathathu. isisombululo elula le ngxaki, ukuba uyazi imithetho, imithetho kunye elikuwo theory lilonke.

Phambi kokuba ubona isisombululo, zama ukucombulula ngokwabo. Siyazi ukuba eli nani lokugqibela inokuba ukusuka kwiqanda ukuya elithoba, kuba abangama lwamaxabiso ezilishumi. score kwenzeke efunekayo ngu 1/10.

Okulandelayo kufuneka ukuba siqwalasele iindlela imvelaphi iziganeko, makhe sicinge ukuba le nkwenkwe thelekelwayo ekunene kwaye waphumelela ngasekunene, amathuba iziganeko ezinjalo ilingana 1/10. Le ukhetho yesibini: isiliphu umnxeba yokuqala, kwaye eyesibini target. Thina ukubala amathuba iziganeko ezinjalo: 9/10 liphindaphindwe 1/9 ekugqibeleni sifumana njengoko 1/10. Umba: ikhwelo yokuqala neyesibini yajika kuba kwidilesi engalunganga, kuphela inkwenkwe sesithathu kulapho wayefuna. Bala amathuba iziganeko ezinjalo: 9/10 iphinda phindiweyo ngo 8/9 kunye 1/8, thina masifumane ngenxa 1/10. Olunye ukhetho kwi imeko ingxaki thina abanomdla, oku kusahleli ukuba walala phantsi kwezi ziphumo, ekugqibeleni sibe 3/10. Impendulo: Amathuba ukuba mfana ndingabizi ezingaphezu kwesithathu amaxesha, ilingana no 0.3.

Amakhadi aneenombolo

Phambi kokuba amakhadi ezisithoba, nganye ibhalwe inani ukusuka kwelinye ukuya elithoba, amanani aziphindwanga. Bamisa ebhokisini uze axutywe kakuhle. Kufuneka ukubala kungenzeka lowo

• waqengqela an inani;
• a-nemivo ezimbini.

Ngaphambi kokuqhubeka kwisigqibo ichaza ukuba m - linani lamatyala yimpumelelo, kwaye n - linani lilonke ongazikhetha. Makhe sifumane kungenzeka ukuba inani lilingene. Ngaba kunzima ukubala ukuba namanani ezine, yaye m wethu, zonke iinketho ezisithoba kunokwenzeka, oko kukuthi, m = 9. Ngoko ke amathuba ilingana ukuya 0,44 okanye 4/9.

Siqwalasela imeko yesibini, inani zabo ezilithoba, kwaye ibe ukuphumelela maxa onke, oko kukuthi, m ngu zero. Amathuba ukuba ikhadi side izakuqulatha inombolo enamanani-mbini, njengoko zero.