Магадлалын онол

Singulaerwert_zerlegung · 1-р сар.06.04 8:43 pm

Neg amarhan bodlogo. Harsan chin bagadaa helheenii eserguutsel boddog baisan sanaand orchihloo. Tostoi yum

Neg tsahilgaan helhee ogogdson baig.


      |-----R1-----|------R4-----|
      |            |             |
A ----            R3             ---- B 
      |            |             |
      |-----R2------------R5-----|

R1 ni 0.95 R2 ni 0.90 R3 ni 0.98 R4 ni 0.92 R5 ni 0.95 iin naidvartai
ajildag gej uzii.

A bolon B iin hoorond tog damjij baival ene helheeg ajillaj baina gej bodii. tegvel ene helhee her naidvartai ajillah iig bodoj ol.

Eichhoernchen · 1-р сар.06.04 9:27 pm

Singulaerwert_zerlegung написал:Neg amarhan bodlogo. Harsan chin bagadaa helheenii eserguutsel boddog baisan sanaand orchihloo. Tostoi yum

Neg tsahilgaan helhee ogogdson baig.
Код: Бүгдийг сонгох
      |-----R1-----|------R4-----|
      |            |             |
A ----            R3             ---- B 
      |            |             |
      |-----R2------------R5-----|
R1 ni 0.95 R2 ni 0.90 R3 ni 0.98 R4 ni 0.92 R5 ni 0.95 iin naidvartai
ajildag gej uzii.

A bolon B iin hoorond tog damjij baival ene helheeg ajillaj baina gej bodii. tegvel ene helhee her naidvartai ajillah iig bodoj ol.

Toglomoor sanagdchlaa. Nemeed simulation program-g bich. :D Tegeed simulation-ii hariug onoliin hariutaigaa tulga. Uund: Simulation hiih iteration-ii toog 100, 1000, 1000, 10000, 100000 geh meteer oorchlood her oirtoj baigaag shalgaval hamgiin sain bolno.

Singulaerwert_zerlegung · 1-р сар.07.04 2:09 am

Hm ....

Код: Бүгдийг сонгох

public class Helhee{
	int davtalt;
	Eserguutsel R1,R2,R3,R4,R5;

	public Helhee(int davtalt){
		this.davtalt = davtalt;
		R1 = new Eserguutsel(95);
		R2 = new Eserguutsel(90);
		R3 = new Eserguutsel(98);
		R4 = new Eserguutsel(92);
		R5 = new Eserguutsel(95);
	}

	public boolean ajillajBainaUu(){

		boolean p1 = R1.ajillajBainaUu();
		boolean p2 = R2.ajillajBainaUu();
		boolean p3 = R3.ajillajBainaUu();
		boolean p4 = R4.ajillajBainaUu();
		boolean p5 = R5.ajillajBainaUu();
		return (p1 && (p4 || (p3 && p5) )) || (p2 && (p5 || (p3 && p4) ));

	}

	public void start(){
		int ok=0;

		for(int i=0;i<davtalt;i++)
			if(this.ajillajBainaUu()) ok++;

		float fok = ((float)ok * (100.0f/(float)davtalt));
		System.out.println("Helhee "+fok+"% huvi naidvartai ajillaj baina");
	}

	public static void main(String [] args){
		int davtalt = 1000000;
		Helhee h = new Helhee(davtalt);
		h.start();
	}
}

class Eserguutsel{
	int ajillagaa;
	Random r;

	public Eserguutsel(int ajillagaa){
		this.ajillagaa = ajillagaa;
		r = new Random();
	}

	public boolean ajillajBainaUu(){
		int i = r.nextInt(100)+1;
		if(i<= ajillagaa) return true;
		return false;
	}

}

Dundjaar 99,42% baih shig baina ...

Eichhoernchen · 1-р сар.07.04 2:58 am

Singulaerwert_zerlegung написал:

Код: Бүгдийг сонгох


      |-----R1-----|------R4-----|
      |            |             |
A ----            R3             ---- B 
      |            |             |
      |-----R2------------R5-----|

pi = P(Ri="on") (i = 1...5) gej temdegleye. qi = 1 - pi

P(AB="on" | R3="on") = p3(1-q1q2)(1-q4q5) = 0.9712
P(AB="on" | R3="off") = q3(p1p4+p2p5-p1p2p4p5) = 0.019625

P(AB="on") = P(AB="on" | R3="on") + P(AB="off"|R3="off") = 0.990834

za · Бичлэг Бичсэн za » 1-р сар.07.04 3:22 am

R1+R4 ued-> 0,397823

R2+R5 ued-> 0,393617 ->hamgiin bagadaa gej oilgoloo

-

Singulaerwert_zerlegung · 1-р сар.07.04 3:38 am

Aibo написал:
Singulaerwert_zerlegung написал:
Код: Бүгдийг сонгох
      |-----R1-----|------R4-----|
      |            |             |
A ----            R3             ---- B 
      |            |             |
      |-----R2------------R5-----|
pi = P(Ri="on") (i = 1...5) gej temdegleye. qi = 1 - pi

P(AB="on" | R3="on") = p3(1-q1q2)(1-q4q5) = 0.9712
P(AB="on" | R3="off") = q3(p1p4+p2p5-p1p2p4p5) = 0.019625

P(AB="on") = P(AB="on" | R3="on") + P(AB="off"|R3="off") = 0.990834

Bi bolon prograam hoyor 99.42% gesen hariu gargaad baih yum aa. Ai messengert alga uu?

Singulaerwert_zerlegung · 1-р сар.07.04 3:59 am

Код: Бүгдийг сонгох

       |-----R1-----|------R4-----| 
       |            |             |
       |            |---R3---R5---| 
       |                          |	
 A ----|                          |---- B 
       |                          |
       |            |---R3---R4---| 
       |            |             |
       |-----R2-----|------R5-----|

Ingej boloh bolov uu?

leuffi · 1-р сар.07.04 4:23 am

Singulaerwert_zerlegung написал:

Код: Бүгдийг сонгох

       |-----R1-----|------R4-----| 
       |            |             |
       |            |---R3---R5---| 
       |                          |	
 A ----|                          |---- B 
       |                          |
       |            |---R3---R4---| 
       |            |             |
       |-----R2-----|------R5-----|

Ingej boloh bolov uu?

bolno. gehdee chi magadlalaa bodohdoo

Код: Бүгдийг сонгох

       |-----R1-----|------R4-----| 
       |            |             |
       |            |---R3---R5---| 
       |                          |	
 A ----|                          |---- B 
       |                          |
       |            |---R6---R4---| 
       |            |             |
       |-----R2-----|------R5-----|

p6=p3

geed bodchihson baina. Aibogiin hariu zuv bh shig bna.

Singulaerwert_zerlegung · 1-р сар.07.04 11:43 pm

Singulaerwert_zerlegung написал:

Код: Бүгдийг сонгох

       |-----R1-----|------R4-----| 
       |            |             |
       |            |---R3---R5---| 
       |                          |	
 A ----|                          |---- B 
       |                          |
       |            |---R3---R4---| 
       |            |             |
       |-----R2-----|------R5-----|

Ingej boloh bolov uu?

Код: Бүгдийг сонгох

P(x+y)=P(x)+P(y)-P(x*y) bolon P(x*y) = P(x)*P(y) iig ashiglaval
P(AB) = P( R1*(R3*R5+R4)+ R2 *(R3*R4+R5)) 
      = P(R1*(R3*R5+R4))+P(R2 *(R3*R4+R5))- P(R1*(R3*R5+R4))*P(R2 *(R3*R4+R5))

ehleed 
P(R1*(R3*R5+R4)) = P(R1)*(P(R3)*P(R5)+P(R4)-P(R3)*P(R5)*P(R4))
P(R2*(R3*R4+R5)) = P(R2)*(P(R3)*P(R4)+P(R5)-P(R3)*P(R4)*P(R5))
gedgiig ashiglahaar 
P(AB) = 0.9942 toi garaad baina ...

Singulaerwert_zerlegung · 1-р сар.07.04 11:52 pm

ingej bodoj bolohgui ch yum uu?

Код: Бүгдийг сонгох

P(x*x) != P(x)*P(x)

gedgiig bodoltsoj uzeegui yum shig baina. hm ...
Teheer ehleed P( ... ) dotorhiigoo bugdiig ni urjuulj baigaad zadalval ?

Eichhoernchen · 1-р сар.08.04 12:03 am

Program(C hel) :

Код: Бүгдийг сонгох

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

int RValues[6] = {0, 95, 90, 98, 92, 95};  // The 1st element is dummy

int Prob(int r)  // Probability
{
  int p = random()%100;
  return (p < RValues[r]);
}

int Check() // Is working circuit?
{
  if (Prob(3)) {
    return (Prob(1) || Prob(2)) && (Prob(4) || Prob(5));
  } else {
    return (Prob(1) && Prob(4)) || (Prob(2) && Prob(5));
  }
}

void Run(int MaxStep)
{
  int Step = 0;
  int Count = 0;
  while (Step < MaxStep) {
    if (Check())
      Count++;
    Step++;
  }
  printf("%i/%i = %f\n", Count, Step, (double)Count/Step);
}

int main(int argc, char *argv[])
{
  int MaxStep;

  assert(argc > 1);
  assert((MaxStep = atoi(argv[1])) > 1);
  Run(MaxStep);

  return 0;
}

Ur dun:

Код: Бүгдийг сонгох

10/10 = 1.000000
99/100 = 0.990000
986/1000 = 0.986000
9908/10000 = 0.990800
99081/100000 = 0.990810
990784/1000000 = 0.990784
9908083/10000000 = 0.990808
99081314/100000000 = 0.990813
990824135/1000000000 = 0.990824

ps: Suulchiin ur dung gargahiin tuld iimerhuu hugatsaa zartsuulav. Sanasnaas udaan baina shuu.
./circuit 1000000000 221.20s user 0.07s system 95% cpu 3:50.54 total

leuffi · 1-р сар.08.04 3:45 am

hehe Singulaerwert_zerlegung programmaa yaaj ajilluulsan yum be? Miniiheer bolhoor Aibo ta 2iinh taaraad baisht.

Aibogiin programmiig ingej uurchilye:

Код: Бүгдийг сонгох

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

int RValues[6] = {0, 95, 90, 98, 92, 95};  // The 1st element is dummy

int Prob(int r)  // Probability
{
  int p = random()%100;
  return (p < RValues[r]);
}

int Aibo() // Aibo-iin arga
{
  if (Prob(3)) {
    return (Prob(1) || Prob(2)) && (Prob(4) || Prob(5));
  } else {
    return (Prob(1) && Prob(4)) || (Prob(2) && Prob(5));
  }
}

int Singulaerwert_zerlegung() // Singulaerwert_zerlegung-iin arga
{
  int p3 = Prob(3);
  int p4 = Prob(4);
  int p5 = Prob(5);
  return (Prob(1) && ((p3 && p5) || p4)) || (Prob(2) && ((p3 && p4) || p5)); 
}

void Run(int MaxStep)
{
int Step = 0;
int Count1 = 0;
int Count2 = 0;
while (Step < MaxStep) {
if (Aibo()) Count1++;
if (Singulaerwert_zerlegung()) Count2++;
     Step++;
     }
printf("Alhamiin too: %i\n", Step);
printf("Aibo: %f\n", (double)Count1/Step);
printf("Singulaerwert_zerlegung: %f\n", (double)Count2/Step);
}

int main(int argc, char *argv[])
{
  int MaxStep;

  assert(argc > 1);
  assert((MaxStep = atoi(argv[1])) > 1);
  Run(MaxStep);

  return 0;
}

Ur dun:

Код: Бүгдийг сонгох

Alhamiin too: 1000000
Aibo: 0.990840
Singulaerwert_zerlegung: 0.990858

bolj bna daa. Minii turuun helsneer chinii hoyor R3 chine uur tuluvt baij bolood baigaan bish u? Magadlalaa lav tegj bodson baih shig baisan.

Bishrelt · 2-р сар.21.04 5:10 pm

miniikheer 99.96 garakh ium. perhaps something is wrong with mine?. ternees gadna garuud code-iinhoo layout-iig iaj oruulaad bainaa. bi paste hiisen bugd left indent bolchihood layout n aldagdchihaad baih ium.

PROGRAM OUTPUT
Probability that system works is: 99.960193.

Press any key to continue . . .

Код: Бүгдийг сонгох

#include <stdio.h>
#include <stdlib.h>
#define NEWLINE printf("\n");

int main ()
{

	//probability of individual gates
    double r1 = 0.95;
	double r2 = 0.90;
	double r3 = 0.98;
	double r4 = 0.92;
	double r5 = 0.95;

    //probability of subsystems works. let subsystem be a each of the serial connections that makes the whole system work.
    double sub1 = r1 * r4;
	double sub2 = r2 * r5;
	double sub3 = r1 * r3 * r5;
	double sub4 = r2 * r3 * r4;
	
	//system fails if and only if all of the subsystem fails
	double system_failure = (1 - sub1) * (1 - sub2) * (1 - sub3) * (1 - sub4);

	//system works if at least one of the subsystem works where (P(X>=1) = 1- (P(0)))
	double system_works = 1 - system_failure;

	NEWLINE 
	
	printf("Probability that system works is: %0.06f.\n", system_works * 100);

	NEWLINE

	system("PAUSE");
	return 0;
}

Eichhoernchen · 2-р сар.22.04 1:57 pm

Bishrelt написал:miniikheer 99.96 garakh ium. perhaps something is wrong with mine?. ternees gadna garuud code-iinhoo layout-iig iaj oruulaad bainaa. bi paste hiisen bugd left indent bolchihood layout n aldagdchihaad baih ium.

PROGRAM OUTPUT
Probability that system works is: 99.960193.

Press any key to continue . . .

Ingej bodson nohtsold program bichih hereg barag baihgui l dee. Simulation bicheed uzeech...

Код: Бүгдийг сонгох

    //probability of subsystems works. let subsystem be a each of the 
    //serial connections that makes the whole system work.
            double sub1 = r1 * r4;
	double sub2 = r2 * r5;
	double sub3 = r1 * r3 * r5;
	double sub4 = r2 * r3 * r4;
	
	//system fails if and only if all of the subsystem fails
	double system_failure = (1 - sub1) * (1 - sub2) * (1 - sub3) * (1 - sub4);

	//system works if at least one of the subsystem works where (P(X>=1) = 1- (P(0)))
	double system_works = 1 - system_failure;

Tegeed chinii program dah ene hesgiig sain oilgohgui baina. Tomiyoogoo tailbarlaach.

Bas chinii source-d TAB neleen baidag baih... Bi bol emacs deer bichdeg bolohoor, shuud copy&paste hiihed zugeer baidag. Herev chi Borland-n C torliin yum ashiglaj baigaa bol Using Tab insteed space ch biluu neg tohirgoo baigaa. Arilgachihval tuunees hoish TAB ashiglahaa bolino. Baigaa TAB bol yaalt ch ugui baih.

Bishrelt · 2-р сар.22.04 9:19 pm

buruu ium shig biana. dahiad neg suuld oroldohoos

Bishrelt · 2-р сар.27.04 11:10 am

Za iim negen bodlogo baina.

Baraa huvarilaltan deer irj bui baraanuudiig hoyor shalgagch hianaj baiv. Baraa tus buriig hoyor hianagch hianana gej bodii. Ehnii shalgagch defecttei baraanii 90 huviig ilruulj chadna. Hoyor dakh shalgagch ch gesen 90%. Ene hoyor shalgagchiin iadaj ali neg n (at least one of them) buh defecttei baraanii 20%-iig n ilruulelgui unguruuh magadlaltai. tegvel doorhiig bod.

a. zuvhun ehnii shalgagch l defecttei baraag ilruulekh magadlal. (prob that only first inspector detects)
hoyor shalgagchiin neg n l defecttei baraag ilruulekh magadlal
(exaclt one of them detects)

b. duriin songoson gurvan baraa n ali ch shalgagchaar haraand urtuugui baih magadlal. (baraa tur buriin shalgalt ilruulelt n bie biendee iamar negen hamaaralgui bol n. that is: neg defecttei baraag ilruulekhed ene n uur iamar negen baraag ilruulekhed iamar ch medeelel uguhgui buiu hamaaralgui)

hariu n ingej garsan biana.
a. 0.10, 0.20
b. 0

Eichhoernchen · 2-р сар.27.04 5:26 pm

Bishrelt написал: Ene hoyor shalgagchiin iadaj ali neg n (at least one of them) buh defecttei baraanii 20%-iig n ilruulelgui unguruuh magadlaltai. tegvel doorhiig bod.

Ene oguulber neg l bishee... 90% gej garchaad baihad 20%-g aldana gedeg... Harin 100n baraanaas 20-g aldah magadlal gevel ali alind ni baij l taarna... Tiimees ene nohtsol-g orhiv.

Bishrelt написал: Baraa huvarilaltan deer irj bui baraanuudiig hoyor shalgagch hianaj baiv. Baraa tus buriig hoyor hianagch hianana gej bodii. Ehnii shalgagch defecttei baraanii 90 huviig ilruulj chadna. Hoyor dakh shalgagch ch gesen 90%. Ene hoyor shalgagchiin iadaj ali neg n (at least one of them) buh defecttei baraanii 20%-iig n ilruulelgui unguruuh magadlaltai. tegvel doorhiig bod.

a. zuvhun ehnii shalgagch l defecttei baraag ilruulekh magadlal. (prob that only first inspector detects)
hoyor shalgagchiin neg n l defecttei baraag ilruulekh magadlal
(exaclt one of them detects)

a. 0.10, 0.20

2 shalgagchiin huvid
p = P(ilruuleh) = 0.9 q = P(aldah) = 0.1
ba 2 shalgagch tus tusdaa ajillah tul, 2 shalgagchiin ilruuleh/aldah ni hariltsan hamaaralgui uzegdel bolno.

Medeej 0.9 bolno.
Harin 2-r shalgagch aldaad 1-r ilruuleh magadlal p*q = 0.09 bolno. Gedgees 2-r urjuulbel 0.18 bolno. (0.20 bish)

Ooroor bas ingej bodoj bolno. Niit magadlalaas "2 shalgagch 2ulaa ilruuleh ba aldah" -g hasch bolno.
1- p*p - q*q = 1 - 0.81 - 0.01 = 0.18

Bishrelt написал: Baraa huvarilaltan deer irj bui baraanuudiig hoyor shalgagch hianaj baiv. Baraa tus buriig hoyor hianagch hianana gej bodii. Ehnii shalgagch defecttei baraanii 90 huviig ilruulj chadna. Hoyor dakh shalgagch ch gesen 90%. Ene hoyor shalgagchiin iadaj ali neg n (at least one of them) buh defecttei baraanii 20%-iig n ilruulelgui unguruuh magadlaltai. tegvel doorhiig bod.

b. duriin songoson gurvan baraa n ali ch shalgagchaar haraand urtuugui baih magadlal. (baraa tur buriin shalgalt ilruulelt n bie biendee iamar negen hamaaralgui bol n. that is: neg defecttei baraag ilruulekhed ene n uur iamar negen baraag ilruulekhed iamar ch medeelel uguhgui buiu hamaaralgui)

b. 0

Magadlal yarij baihad 0 bolno gedeg ch dee... hehe
q * q = 0.01 bolno.

ps: Deerh toonuudiig taslalaas hoish 1 ornii nariivchlaltai bodvol deerh hariunuud garah bolno. Gevch uchir dutagdaltai gej bodnom...

Bishrelt · 2-р сар.28.04 1:55 am

miniikh bas chiniikh shig oiroltsoo garchaad bolj uhgui baina. harin 20% gedeg n harin bur no-toi sanagdaad baigam. nom n aldaata m boluu.

A = ehnii shalgagch amjilttai ilruulev. = 0.9
B = hoyor dakhi n amjiltai ilruulev. = 0.9
A` = ehnii shalgagch ilruulsengui = 0.1
B` = hoyor dakhi shalgagch ilruulsengui -= 0.1

a. 1. A^B + A^`B = 0.81+0.9 = 0.9
2. A^B` + `A^B = 0.9 + 0.9 = 0.18

b. `A^`B = 0.1^2 = 0.01

za uur enentei iag adilkhan gehdee arai iavdaltai neg bodlogo baina.

doloo honogiin 1 negdehees 5 udur (MON-FRI) tus bur ekhnii baraa hangamjaas udurt neg bagts baraa irjdeg baiv.
Hoyor dakhi baraa hangamjaas doloo honogiin 2 udurt, udur tus bur 1 bagts baraa irdeg baiv.
Uuruur helvel ehnii hangamjaas doloo honogt tavan baraa, hoyordakhaas doloo honogt 2 baraa irdeg baiv.
Hagas sain buten sain amraltiin udur tul uuniig bodlogond avch heleltsehgui bolno.

Buh orj irj baigaa bagts baraanii 80% n shalgaltaar tentsej, harin 1 ehnii hangamjaas irsen baraanii 90% n shalgaltaar tentsjee.
Tegvel duriin negen udur (negees tavdakhiin ali neg n), ter udurt orj irsen hoyor baraa hoyolaa tentsekh magadlal her ve? :)
enen deer mun adil ehnii bagts baraa n shalgaltaar tentsekh n hoyor dakhi baraanii tentsekh esekhed ogt hamaaralgui bolno.

DaKid · 10-р сар.16.04 5:47 am

Za end Magadlaliin onoliin bodlogo tavii!

Mathematic sonirhdog gishuudee idevhtei oroltsooroi gej husii!

DaKid · 10-р сар.16.04 5:50 am

A box contains 4 red, 3 black, 2 green and 1 white ball. A ball is drawn from the box and then returned to the box. What is the probability that the ball will be (a) red, (b) red or black?

Amethyst Goddess · 10-р сар.16.04 11:12 pm

a. 0.4
b. 0.7
zuv uu

Зочин · 10-р сар.17.04 6:40 pm

DaKid написал:A box contains 4 red, 3 black, 2 green and 1 white ball. A ball is drawn from the box and then returned to the box. What is the probability that the ball will be (a) red, (b) red or black?

a) 4/10=0.4
b) 0.4+0.3=0.7

DaKid · 10-р сар.20.04 7:56 am

Zaa tegeheer Amethyst zov bodjee!
ene ni a) 4/10
b) 7/10 baih yum

DaKid · 10-р сар.20.04 7:58 am

Neg ail 6 huuhedtei baiv. Ene ailiin niit 6 huuhed bugd huu esvel ohin baih magadlaliig bod!

Amethyst Goddess · 10-р сар.20.04 4:57 pm

2* (1/6)^6

Eichhoernchen · 10-р сар.26.04 3:45 pm

Anonymous написал:bodlogoo chi hundruuleegui barag hyalbarchlaad tavichihaj. bodlogiig chin arai goe bolgood ogeo.

yadahdaa 3 eregtei huuhedtei baih magadlaliig ol.

N eregtei huuhedtei baih magadlaliig P(N) geye.
Yag 3n eregtei huuhedtei baih magadlal. P(3) = C(6,3)/2^6
Yag 4n eregtei huuhedtei baih magadlal. P(4) = C(6,4)/2^6
Yag 5n eregtei huuhedtei baih magadlal. P(5) = C(6,5)/2^6
Yag 6n eregtei huuhedtei baih magadlal. P(6) = C(6,6)/2^6

Edgeeriig nembel bidnii heregtei hariu garna.
Gehdee eniig tsootsoolohiin omno hariug ooroor bodoyo l doo. Yadaj 3n eregtei huuhedtei gedgiin esreg oguulber ail 2 -oos tsoon eregtei huuhedtei bolno. Tegvel Ene tohioldol doh magadlal P(0)+P(1)+P(2) bolno. Endees yadaj 3n eregtei huuhedtei baih magadlal 1-P(0)-P(1)-P(2) bolno. Deerhees arai tsoon uildeltei.

ps: C(6, 3) ni 6gaas 3 aar avsan heseglel bolno.
ps2: Amidral deer eregtei huuhed toroh magadlal 0.51 orchim gedeg baih shuu.

#AsuultSambar :

Магадлалын онол

Magadlal iin bodlogo , 1

Re: Magadlal iin bodlogo , 1

simulation

Re: Magadlal iin bodlogo , 1

Re: Magadlal iin bodlogo , 1

Minii program neg iimerhuu bolloo

Магадлалтай бодлого

Re: PROBABILITY BODLOGO

Магадлалын онол

1 bodlogo

Re: 1 bodlogo

Bas 1 bodlogo