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2008~2009第一學期

（閉卷）

NameStudentIDClass

Date:Jan8,2009Time:8:30amto11:00am

Instruction:Answerallquestionsinthespaceprovided.Showyourwork.

Question

1

2

3

4

5

6

7

8

total

Mark

Score

Question1(21points)Fillingtheblanks

Signature

(1).LetA,Bbetwoevents,P(A)=0.4，P(B)=0.3，P()=0.6，thenP()=.

(2).Supposearandomvariablehastheprobabilitydistributionwith,then=.

(3).Supposehasthejointdensityfunction,thenthemarginaldistributionforalone=.

(4).Suppose，consideraquadraticequationwithoneunknownabouty,iftheprobabilityofthisequationhavingnorealrootis,then.

(5).Thenumberofdistinctpermutationscanbemadefromthelettersofthewordaccess=.

(6).Letbearandomsampleofsizentakenfrompopulation,,then.

(7).Letbearandomsampleofsizentakenfrompopulation,andareunknown,ifisaconfidenceintervalforwithconfidencelevel,thenk=.

Score

Question2(18points)Choosingtheonlyonerightresult

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(1).Suppose,,ifandareindependent,then()

(A) (B)

(C) (D)

(2).SupposeX~N(,)，Y~E(),findtheerrorresult()

(A) (B)

(C)(D)

(3).Supposethatrandomvariablesandareindependent,iftheyhavethesame

probabilitydistributionwith,then()

(A)2/3 (B)1 (C)1/2 (D)5/9

(4).Suppose,and,if,

then()

(A)< (B)>(C)< (D)>

(5).Letbearandomsampleofsizentakenfrompopulation,，，，,thenthefollowingrandomvariableswhichoneisthet-distributionwithn-1degreesoffreedom.()

(A) (B)(C) (D)

(6).Suppose,,then=()

(A)1(B)-1(C)1/2(D)0

Score

Question3:(12points)

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SupposearandomvariableXhasthedensityfunction.Observeindependentlyforthreetimes,letdenotethenumberofaneventoccurringinthreetimes,determine:

(1)theprobabilitydistributionof;

(2)theprobabilitydistributionof.

Score

Question4(14points)

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Supposehasthejointdensityfunctionasfollows:

.

(1)Findtheconstantc;

(2)AreXandYindependent?

(3)DeterminetheconditionaldistributionofXforanygivenvalueofY.

(4)

Score

Question5(10points)

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Supposethataboxcontainsonefaircoinandonecoinwithaheadoneachside.Supposealsothatonecoinisselectedatrandomandtossed,aheadisobtained.Determine:

(1)theprobabilityofthiseventoccurring;

(2)theprobabilitythatthiscoinisthefaircoinwhentheaboveeventoccurred.

Score

Question6(5points)

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Thereare4girlsand8boystakepartininterviewofsomecompany.Supposethattheinterviewerselectonestudentrandomlyeverytime,determinetheprobabilitythattherearejust2boyswaitingforinterviewingwhenallthegirlshaveinterviewed.

Score

Question7(12points)

Signature

SupposearandomvariableXhasthedensityfunction,let

,

determine:

thejointprobabilitydistributionof(Y,Z);

D(Y+Z).

Score

Question8(8points)

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