BI TP IU KIN

MN: XC SUT THNG K

Cu 1: c nhp kho, sn phm ca nh my phi qua 3 vng kim tra cht lng c lp nhau. Xc sut pht hin ra ph phm cc vng ln lt theo th t l 0,8; 0,9 v 0,99. Tnh xc sut ph phm c nhp kho.Bi gii:

Gi Ai l bin c sn phm qua kim tra cht lng vng th i, i=1,2,3.

Gi B l bin c sn phm ph phm c nhp kho

Ta c :

(B)=

Cu 2: Ba phn xng I, II, III cng sn xut ra mt loi sn phm. T l ph phm do ba phn xng sn xut ra tng ng l . Rt ngu nhin mt sn phm t mt l hng gm 1000 sn phm trong c 500 sn phm do phn xng I, 350 sn phm do phn xng II v 150 sn phm do phn xng III sn xut.

a. Tm xc sut sn phm rt c l ph phm (bin c A).

b. Ly ngu nhin 1 sp tu l hng ph phm.Tnh xc sut ph phm l do phn xng I, II, III sn xut.Bi gii:

Gi A l bin c sn phm rt ra l ph phm

Gi Ai l bin c sn phm c chn ca phn xng th i, i=1,2,3

Theo iu kin u bi cho :

Cc bin c l mt h y do ta p dng cng thc tnh xc sut y :

a. xc sut sn phm rt ra c l ph phm:

EMBED Equation.3 b. Xc sut ph phm l do phn xng I,II,III sn xut

p dng cng thc Bayes:

- Xc sut sn phm ph phm rt ra thuc phn xng I:

- Xc sut sn phm ph phm rt ra thuc phn xng II:

- Xc sut sn phm ph phm rt ra thuc phn xng III:

Cu 3: xc nh chiu cao trung bnh ca cc cy con trong mt vn m ngi ta tin hnh o ngu nhin 40 cy. Kt qu o c nh sau:

Khong chiu cao (cm)16,5-1717-17,517,5-1818-18,518,5-1919-19,5

S cy tng ng 35111263

a. Tm khong tin cy 90% cho chiu cao trung bnh ca vn cy con.

b. Nu mun khong c lng c chnh xc th cn ly mu bao nhiu cy.

Cho bit gi tr ti hn mc 0,05 ca phn b chun tc N(0;1) l 1,64.Bi gii:

Theo u bi ta c kt qu theo bng sau:

X

EMBED Equation.3

EMBED Equation.3

16,5-17316,75-0,3-0,90,090,27

17-17,5517,25-0,2-10,040,2

17,5-181117,75-0,1-1,10,010,11

18-18,51218,250000

18,5-19618,750,10,60,010,06

19-19,5319,250,20,60,040,12

40-1,80,76

chn ,h=5

a. Khong tin cy 90%:

b. Kch thc mu cn thit c l:

Chn n=117Cu 4: Cho l hai bin ngu nhin ri rc c phn b xc sut

a. Tnh k vng , .

b. Tnh phng sai , .

c. Tnh xc sut , k vng v phng sai nu , c lp.

Bi gii:

a. K vng EX, EY:

EX = 0.0,15+1.0,30+2.0,25+3.020+4.0,08+5.0,02 = 1,82

EY = 0.0,30+1.0,20+2.0,2+3.0,15+4.0,10+5.0,05 = 1,7

b. Phng sai DX, DY:

EX2 = 02.0,15+12.0,30+22.0,25+32.020+42.0,08+52.0,02 = 4,88

DX = EX2 (EX)2 = 4,88 (1,82)2 = 1,5676

EY2 = 02.0,30+12.0,20+22.0,2+32.0,15+42.0,10+52.0,05 = 5,2

DY = EY2 (EY)2 =5,2 (1,7)2 = 2,31

c. - Xc sut: P{X + Y 3}

Ta c: P{X + Y 3}= P{X+Y= 0} + P{X+Y= 1 } +P{X+Y= 2 } +P{X+Y= 3 } .

Vi:

P{X+Y= 0} =P{ X= 0, Y= 0 }=0,0450

P{X+Y= 1} =P{ X= 0, Y= 1 }+P{ X= 1, Y= 0 }= 0,03 + 0,09 = 0,12

P{X+Y= 2} =P{ X= 0, Y= 2 }+P{ X= 1, Y= 1 }+P{ X= 2, Y= 0 }

= 0,03 + 0,06+ 0,075 =0,165

P{X+Y= 3} =P{ X= 0, Y= 3 }+P{ X= 1, Y= 2 }+P{ X= 2, Y= 1 }+ P{X=3,Y=0}

= 0,0225 + 0,06+ 0,05+ 0,06 =0,1925

Nn:

P{X + Y 3}= 0,0450 + 0,12 +0,165 + 0,1925 = 0,5225

- K vng: E(X-Y)

E(X-Y) = EX EY = 1,82 1,7 = 0,12

- Phng sai: D(X-Y) = DX + DY = 1,5676 + 2,31 = 3,8776

EMBED Equation.DSMT4 012345 EMBED Equation.DSMT4 0,150,300,250,200,080,02

EMBED Equation.DSMT4 012345 EMBED Equation.DSMT4 0,300,200,20,150,100,05

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