Магадлалын онол

[hahn]

hyazgaariiin teoremiin batalgaa hiih hun bna uu?
bas ter yavagdaad bgaa lotto 30-6 iin p=?

[hahn]

hyazgaariiin teoremiin batalgaa hiih hun bna uu?
bas ter yavagdaad bgaa lotto 30-6 iin p=?

[jonon hongor]

hyazgaariin teorem gedgiig chini hyazgaariin gol teorem gej oilgoj boloh u?
hyazgaariin gol teorem bol ul hamaarah negen ijil tarhalttai sanamsargui hemjigedhuunii niilber hyazgaartaa normal tarhalttai baidag gesen teorem yum batalgaanii undsen sanaa ni niilber sanamsargui hemjigdehuunii haraktristic funktsiig tayloriin tsuvaand zadlaad hyazgaart shiljihed hyazgaar ni normal tarhaliin haraktristik funkts gardag
ter lotto-g harin sain medehgui yumaa

[jonon hongor]

Unuu boltol bid zoos shidehed suldeeree buuh magadlal 0.5 gej uzseer irsen biz dee. Getel sayhan neg zaluu erdemten ene tiim bish gej bataljeee. Hun zoosiig shidehdee haashaa haruulan barij baisan ter talaaraa unah magadlal 0.51 gesen bna.

magadlaliin onold tuhain uzegdliin zagvart tohiroh gol gol huchin zuiliig avch uzdeg zarim 1 nuluugui shaham uzegdluudiig zagvaraasaa hasdag es tegvees tuhain uzegdliig zagvarchlah ni mash hund bolno tiim bolhoor erdemted zoos too suldeeree buuh magadlal tentsuu 0.5 gej uzsen baih.

[jonon hongor]

kustagiin bodlogo:
Herev 3 herchmee 1-r, 2-r, 3-r gej dugaarlaad 1 ba 2-r herchimiin niilber 3-r herchmiin niilberees ih baih magadlal gej uzeed bodvol
X1~U[0;1]
X2~U[0;1]
X3~U[0;1]
P{gurvaljin uuseh}=P{X1+X2>X3}=3/4
Herev 3 herchmee dugaarlalgui yamarch tohioldold gurvaljin uusne gej uzvel
P{gurvaljin uuseh}=P{(X1+X2>X3)^(X1+X3>X2)^(X2+X3>X2)}=1/4
end: ^-eer dooshoo harsan U buyu ogtloltsoliig temdgellee
ene bodolt zuv ? humuusee

[jonon hongor]

X, Y cx hargalzan ul hamaarah. L1 , L2 parametrtei poisson tarhalttai.
X-iin X+Y=n nuhtsun dehi math dundaj ol. eniig bodotsgoogooroi

za yamarch baisan oroldood uzlee:

E(X/X+Y=n)=sum{k=0,n ; ((L1/L2)^k)*k/(k!*(n-k)!)}/
/sum{k=0,n ; ((L1/L2)^k)/(k!*(n-k)!)}/
end sum{k=0,n ; f(k)}-eer k=0 -s k=n -g duustalh f(k)-uudiin niilberiig temdgellee.

sum{...} niilberiig ni olj chadsangui

ene hariu zuv u?

[@lt@@]

kustagiin bodlogo:
Herev 3 herchmee 1-r, 2-r, 3-r gej dugaarlaad 1 ba 2-r herchimiin niilber 3-r herchmiin niilberees ih baih magadlal gej uzeed bodvol
X1~U[0;1]
X2~U[0;1]
X3~U[0;1]
P{gurvaljin uuseh}=P{X1+X2>X3}=3/4
Herev 3 herchmee dugaarlalgui yamarch tohioldold gurvaljin uusne gej uzvel
P{gurvaljin uuseh}=P{(X1+X2>X3)^(X1+X3>X2)^(X2+X3>X2)}=1/4
end: ^-eer dooshoo harsan U buyu ogtloltsoliig temdgellee
ene bodolt zuv ? humuusee

Tasraltgui tarhalttai bolhoor integral avj l bodogdoh bh gej bodood bna shd.
Ingehed p{X1+X2+X3}=3/4. yagaad iim bolsniig tailbarlaach. sonin sanagdaad baih yum.

[jonon hongor]

kustagiin bodlogo:
Herev 3 herchmee 1-r, 2-r, 3-r gej dugaarlaad 1 ba 2-r herchimiin niilber 3-r herchmiin niilberees ih baih magadlal gej uzeed bodvol
X1~U[0;1]
X2~U[0;1]
X3~U[0;1]
P{gurvaljin uuseh}=P{X1+X2>X3}=3/4
Herev 3 herchmee dugaarlalgui yamarch tohioldold gurvaljin uusne gej uzvel
P{gurvaljin uuseh}=P{(X1+X2>X3)^(X1+X3>X2)^(X2+X3>X2)}=1/4
end: ^-eer dooshoo harsan U buyu ogtloltsoliig temdgellee
ene bodolt zuv ? humuusee

Tasraltgui tarhalttai bolhoor integral avj l bodogdoh bh gej bodood bna shd.
Ingehed p{X1+X2>X3}=3/4. yagaad iim bolsniig tailbarlaach. sonin sanagdaad baih yum.

(x1,x2,x3) ogtorguid negj taltai kub deer X1+X2>X3, 0<=X1<=1, 0<=X1<=1, 0<=X1<=1 mujiig dursleed uzhed shuud haragdana
kubiin ezelhuun=1 (1,0,1), (0,0,1), (0,1,1), (0,0,0) tsegt oroitoi piramid-n ezelhuun = 1/4 iimd deerh mujiin ezelhuun =1-1/4=3/4
gej bodson

[Зочин]

za shaatsgaa shaatsgaa ta nariin magadlal meddeg gej haashaa harsan yum baidiim

[jonon hongor]

field-n bodlogo:
havtgaid 4 tseg shidjee edgeer 4 tsegeer baiguulsan 4 untsugt gudger 4 untsugt baih magadlaliig ol

ene bodlogiig bodoj chadah hun baina u?

minii huvid bol simulation hiij l hariug ni oiroltsoo gargaj bolmoor yum shig baina yag bodoltiig ni hiisen hun baival end bodoltiig ni taviach

[jonon hongor]

a,b,c coefficent-uud U[0,1]-d jigd tarhalttai bol ax^2+bx+c=0 quadratic tegshitgel bodit yazguurtai baih magadlaliig ol

[Eichhoernchen]

a,b,c coefficent-uud U[0,1]-d jigd tarhalttai bol ax^2+bx+c=0 quadratic tegshitgel bodit yazguurtai baih magadlaliig ol

MonteCarlo-dchloo.
Result:

Код: Бүгдийг сонгох

Simulation (    1000 times) result for Monte Carlo method: 0.261000
Simulation (   10000 times) result for Monte Carlo method: 0.248800
Simulation (  100000 times) result for Monte Carlo method: 0.254440
Simulation ( 1000000 times) result for Monte Carlo method: 0.253996
Simulation (10000000 times) result for Monte Carlo method: 0.254614
./a.out  2.12s user 0.00s system 99% cpu 2.139 total

Source (C hel)

Код: Бүгдийг сонгох

#include <stdlib.h>
#include <stdio.h>
#include <math.h>

#define N 5
#define R 9997

double MonteCarlo(int n)
{
  int i;
  int hit = 0;
  int a, b, c;

  for (i = 0; i < n; i++) {
    a = rand()%R;
    b = rand()%R;
    c = rand()%R;

    if (b*b-4*a*c >= 0)
      hit++;
  }

  return (double)hit/n;
}

int main()
{
  int i;
  int a[N] = {1000, 10000, 100000, 1000000, 10000000};

  for (i = 0; i < N; i++)
    printf("Simulation (%8d times) result for Monte Carlo method: %f\n", a[i], MonteCarlo(a[i]));

  return 0;
}

[@lt@@]

Ingehed programchlaliin onoogiin tovshind bodlogiig program bicheed bodoj chadahgui baihaa. Harin tootsoolj bolno. Ooroor helbel programchlaliin odoogiin tovshind program ni hunii bodson algoritmiin daguu l tootsooldog. Mon rand() gesen funkts ni absolute randomiig gargaj chaddaggui. Er ni odoo humuust absolute randomiig gargah engiin algoritm bhgui bgaa gej sonsson yum baina. Harin kvant computeraar absolute randomiig uusgeh algoritm garsan gej sonsson yum baina.

[Eichhoernchen]

Geometer-iin bolon neleen torliin logic bodloguudiig programiin argaar bodoj batalj boldog gedgiig tootsoond oruulj baina uu?

Odoogoor barag absolute gej helj bolmoor random toog uusgej boldog. Uund Computer-iin Hardware-aar demjleg ogohoos gadna, tuhain computer-iin CPU, Keyboard, Mouse bolon mash olon tolviig tootsooldog.

Medeej ooriinhoo programiin tuhai yariagui bolno. Deerh program bol togloom l doo.

[T.G.]

Computer Algebra gej suuliin ued ih hugjij bui matematikiin salbar bna. end bol computer ashiglaj bodlogiin hariug yag gargah arguudiig sudaldag. theoremuudiin batalgaag computeraar shalgadag algorithmuud baidag gej sonsson yum bna. yur ni bol "bodoh", "tootsooloh" 2-iin hoorond hatuu zaag bhgui. hun computer bugd yamar neg algorithmiig dagana. algorithmuud ni zuvhun niilmel baidal, design-aaraa yalgagdana. hund shiidegdeegui shine bodlogo uguhud ter hun munh busiig uzuuleheesee umnu bodoj duusgana gesen yamar ch batalgaa bhgui.

[@lt@@]

Geometer-iin bolon neleen torliin logic bodloguudiig programiin argaar bodoj batalj boldog gedgiig tootsoond oruulj baina uu?

Odoogoor barag absolute gej helj bolmoor random toog uusgej boldog. Uund Computer-iin Hardware-aar demjleg ogohoos gadna, tuhain computer-iin CPU, Keyboard, Mouse bolon mash olon tolviig tootsooldog.

Medeej ooriinhoo programiin tuhai yariagui bolno. Deerh program bol togloom l doo.

Tedgeer bodlogiig bodoh algoritmiig hun bodchood computereer tootsoolliig ni hiilgedeg bhgui yu. Absolute random gargaj chadaagui baigaa l daa. Odoogiin random arga ni galuagiiin onol deer undesledeg gej unshsan yum baina. Ene ni randomd mash oirhon bolovch absolute random hezee ch baij chadahgui.

[@lt@@]

Computer Algebra gej suuliin ued ih hugjij bui matematikiin salbar bna. end bol computer ashiglaj bodlogiin hariug yag gargah arguudiig sudaldag. theoremuudiin batalgaag computeraar shalgadag algorithmuud baidag gej sonsson yum bna. yur ni bol "bodoh", "tootsooloh" 2-iin hoorond hatuu zaag bhgui. hun computer bugd yamar neg algorithmiig dagana. algorithmuud ni zuvhun niilmel baidal, design-aaraa yalgagdana. hund shiidegdeegui shine bodlogo uguhud ter hun munh busiig uzuuleheesee umnu bodoj duusgana gesen yamar ch batalgaa bhgui.

Computer algebr chini undsendee algoritm boddog salbar bhaa. Matematicchid sain medej bgaa bh. Orchin ued matematict tootsoo hiiheesee iluu algoritm bolon invariantiig oloh ni hamgiin chuhal bolson gej bas sonsoj baisan yum baina.
Bodoh tootsooloh 2 hatuu zaagtai yu gedeg asuudal deer 20-r zuunii ehend margaan yavagdaj baisan. Uund logic deer undesledeg heseg erdemted bolon tuunii esreg zon sovin baidag gesen neg hesegiin(Puankare geh met) temtsel ornoson yum. Tegeed etsest ni Geidel biluu neg matematikch zon sovingui matematic bhgui gesen neg teorem batalsan yum bna lee. Uneheer sonin ed l dee. Olonlog setguul deerees unshij baisiin. tiim bolhoor bodoh ni zon sovingiin ur dun, tootsooloh ni logiciin ur dun gej oilgoj boloh taltai. Gehdee tarhinii sudalgaa bolon hiimel oyun uhaanii sudalgaa hogjood ireheer nuuts ni tailagdah biz dee.
Harin sod humuus ter shiidegdeegui shine bodlogiig bodchihdog yum shig baigaan.

[jonon hongor]

a,b,c coefficent-uud U[0,1]-d jigd tarhalttai bol ax^2+bx+c=0 quadratic tegshitgel bodit yazguurtai baih magadlaliig ol

MonteCarlo-dchloo.
Result:

Код: Бүгдийг сонгох

Simulation (    1000 times) result for Monte Carlo method: 0.261000
Simulation (   10000 times) result for Monte Carlo method: 0.248800
Simulation (  100000 times) result for Monte Carlo method: 0.254440
Simulation ( 1000000 times) result for Monte Carlo method: 0.253996
Simulation (10000000 times) result for Monte Carlo method: 0.254614
./a.out  2.12s user 0.00s system 99% cpu 2.139 total

deerh bodlogiin huvid a, b, c- uud ul hamaarah gesen 1 nuhtsul hayachihsan bailee

unendee hariu ni ch simulation-ii toog ihesgevelch garna l daa gehdee ene bodlogiin bodoltiig simulation hiihguigeer tootsooch dee

yag hariu ni (5+3*ln(4))/36=0.254413

[jonon hongor]

Computer Algebr gej baidag yum bilee minii neg tanidag nuhur irland ch biluu yamarch baisan europ-n 1 ulsad master hamgaalchaad irsen deg mathcad prog deer urjver funktsiin ulamjlaliig olood tavichihaj baisan

[(T.G.)]

Computer Algebra gej suuliin ued ih hugjij bui matematikiin salbar bna. end bol computer ashiglaj bodlogiin hariug yag gargah arguudiig sudaldag. theoremuudiin batalgaag computeraar shalgadag algorithmuud baidag gej sonsson yum bna. yur ni bol "bodoh", "tootsooloh" 2-iin hoorond hatuu zaag bhgui. hun computer bugd yamar neg algorithmiig dagana. algorithmuud ni zuvhun niilmel baidal, design-aaraa yalgagdana. hund shiidegdeegui shine bodlogo uguhud ter hun munh busiig uzuuleheesee umnu bodoj duusgana gesen yamar ch batalgaa bhgui.

Computer algebr chini undsendee algoritm boddog salbar bhaa. Matematicchid sain medej bgaa bh. Orchin ued matematict tootsoo hiiheesee iluu algoritm bolon invariantiig oloh ni hamgiin chuhal bolson gej bas sonsoj baisan yum baina.
Bodoh tootsooloh 2 hatuu zaagtai yu gedeg asuudal deer 20-r zuunii ehend margaan yavagdaj baisan. Uund logic deer undesledeg heseg erdemted bolon tuunii esreg zon sovin baidag gesen neg hesegiin(Puankare geh met) temtsel ornoson yum. Tegeed etsest ni Geidel biluu neg matematikch zon sovingui matematic bhgui gesen neg teorem batalsan yum bna lee. Uneheer sonin ed l dee. Olonlog setguul deerees unshij baisiin. tiim bolhoor bodoh ni zon sovingiin ur dun, tootsooloh ni logiciin ur dun gej oilgoj boloh taltai. Gehdee tarhinii sudalgaa bolon hiimel oyun uhaanii sudalgaa hogjood ireheer nuuts ni tailagdah biz dee.
Harin sod humuus ter shiidegdeegui shine bodlogiig bodchihdog yum shig baigaan.

algorithm boddog gej yu gesen ug ve. ter Godel. Roger Penrose tarhi platonik gej nerlegdeh dan matematik medlegees togtson yurtuntstiig shuud mederch tendees medeelel olj avdag gesen yum yariad bgaa. ter yu l bol. oyun uhaaniig sanamsargui toon deer suurilsan heuristik algorithmoor zagvarchilj bolno gej itgeh undeslel bii. tiim aihtar "deed" yum bol bhgui bh. harin "self awareness, consiousness" ene ter bol arai uur baij bagad.

[@lt@@]

Zarim　ug hellegiig oilgohgui baigaad uuchlaarai. (heuristik,self awareness geh met) Algoritm boddog gedeg ni tuhain bodlogiig yamar algoritmaar bodoj boloh ve gedgiig sudlahiig l helsen yum.

[Eichhoernchen]

Heuristic geheer yeronhiidoo zaaval zov baih albagui, yeronhiidoo tiimerhuu baih gesen taamag taviad teruugeeree haih taliin l yumdaa...

Logic bodlogo bodohod lav ashigladag.

Main article Heuristic (computer science)

In computer science, a heuristic is a technique designed to solve a problem that ignores whether the solution is provably correct, but which usually produces a good solution or solves a simpler problem that contains or intersects with the solution of the more complex problem.

Heuristics are intended to gain computational performance or conceptual simplicity potentially at the cost of accuracy or precision.

Source: http://en.wikipedia.org/wiki/Heuristic

[Eichhoernchen]

oyun uhaaniig sanamsargui toon deer suurilsan heuristik algorithmoor zagvarchilj bolno gej itgeh undeslel bii. tiim aihtar "deed" yum bol bhgui bh. harin "self awareness, consiousness" ene ter bol arai uur baij bagad.

sanamsargui too gedeg yu l bol... Ter undselelee bichdee?
Deed yum baihgui ch baij magad. Teriig "burhan" l medeh baihdaa.

[Eichhoernchen]

naad zahiin undeslel gevel P ni BPP-iin ded olonlog bolno

yostoi oilgomjgui yaridag baishd.

Arai todorhoi, t*n*g hun ch oilgohoor tailbarlaad ogooch. plz.
Aahn tiim bas, Neuron -tai yaaj holbogdoh tuhai geed...

[DaKid]

Usa-d iher huuhed toroh magadlaliig 1/90 gej uzjee, Oooroor helbel 90 eh torohod 1 eh iher huuhed gargah magadlaltai gej uzvel,
1. 30 eh torohod yadaj 1 eh iher huuhed toruuleh magadlaliig ol?
2. 100 eh torohod iher huuhed toroh magadlal mon herhen oorchlogdoh ve?

[DaKid]

Ehnii tohioldol buyu 30 ehed yadaj 1 iher toroh magadlal ni 1/270 buyu,
p=0.00373 mon uu?