工程数学(三)概率统计离散数学

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1、工程数学（三）概率统计离散数学Chapter3randomvariablesandtheirdistributionsIfwecareabouteventsA={nodefective},B={atleast2piecesofdefective},C=}{nomorethankAdefectiveproduct,theA,B,CcanseparatelyinYisexpressedasArandomvariableA二{e

2、,Y(e)=0},B={e

3、Y(e)=2},C={e

4、Y(e)islesstha

5、norequaltok}・Forconvenience,usuallysavesintheeventsaidthee,whichcanbeexpressedasA二{Y二0},B二2}{Yp,C二{Ykorless}・valuesofArandomvariablewiththetestresults,can，tpredictwhatittakebeforethetestvalues,anditsvaluehasAcertainprobability,sorandomvariableswithnormal

6、functionhasessentialdifference・Theintroductionofarandomvariable,sothatwecanuserandomvariablestodescribethestochasticphenomenon,thereforemayusethemethodofdifferentialandintegralcalculustoin-depthstudytheresultsofrandomizedtrials・Thedistributionfunctionoft

7、herandomvariableDefine3.2Xisa:randomvariable,Xisanyrealnumber,thefunctionevaluatedat[0,1]FofxisequaltoPofxislessthanorequaltox,minusinfinityislessthanxIt'scalledthedistributionfunctionofrandomvariableX.Foranyrealnumber1x,2x(1x

8、P(xx2orless)-P(xxorless1)=F(x2)-F1(x)・(3.1)Asaresult,ifknowndistributionfunctionofX,knewXfallatanyinterval(1X,2X]ontheprobability,inthissense,thedistributionfunctioncompletelydescribethestatisticalregularityofrandomvariables・Thedistributionfunctionisanor

9、malfunction,anditcanbeusedtostudyrandomvariablesincalculus・IfyouviewXasthecoordinateoftherandompointonthenumberline,thenthefunctionofthedistributionfunctionF(X)atXistheprobabilitythatXfallsintheinterval(-infinity,X).CasesofarandomvariableX3.3allpossiblev

10、alueforX1二1,X二2,2X3=3.Theevents1}{X二X(I二1,2,3)theprobabilityofP二P(X二1)1二14,p二二p(X二2)2二12,p二:p(X:=3)3二14,PX12orless,P32

11、X)isthecumulativeprobabilityvalueXXorless,theprobabilityofadditivitylimitedknowledge,itislessthanorequaltoXXthesumoftheprobabilitypkk・ThusthereareF(x)=0,x<-1,SoPofXisnegative1,negative1islessthanorequaltoX<2,PofXisequalton