2009쓪4퓂새랻쪦랶톧풺톧놨(ퟔ좻뿆톧냦)뗚9뻭뗚2웚JournalofLangfangTeachersCollege(NaturnalScienceEdition)룅싊춳볆퓚뺭볃톧훐뗄펦폃틗퇞뒺ꆡ컢탛(뫢퇴쪦랶톧풺,뫾쓏뫢퇴421008)ꆾ햪ꆡ튪ꆿꆡ춨맽쪵샽쳖싛룅싊춳볆퓚뺭볃맜샭뻶닟ꆢ뺭볃쯰쪧맀볆ꆢퟮ듳뺭볃샻죳쟳뷢ꆢ뺭볃놣쿕ꆢ뺭볃풤닢뗈뺭볃톧컊쳢훐뗄펦폃ꆣꆾ맘볼듊ꆿꆡ룅싊춳볆;뺭볃톧;펦폃ApplicationofProbabilityandStatisticsintheEconomicsYIYan2chunꆡWUXiong2taoꆾAbstractꆿꆡThistextdiscussesafewapplicationsofprobabilityandstatisticsonsomeeconomicsproblemsthroughsomeconcreteexamples,suchaseconomicmanagement,theestimationofeconomylost,thesolvingofthebiggesteconomicprofits,economicinsuranceetc.ꆾKeywordsꆿꆡprobabilityandstatistics;economics;applicationꆲ훐춼럖샠뫅ꆳꆡꆡꆡꆡꆲ컄쿗뇪쪶싫ꆳAꆡꆡꆡꆡꆲ컄헂뇠뫅ꆳ1674-3229(2009)02-0089-03ꆡꆡ룅싊춳볆쫇튻쏅쿠떱폐좤뗄쫽톧럖횧톧뿆ꆣ쯦싊춳볆횪쪶뿉틔믱뗃뫏샭뗄뻶닟,듓뛸쪵쿖헢룶쒿ퟅ뿆톧벼쫵뗄랢햹뫍볆쯣믺뗄웕벰,쯼ퟮ뷼벸쪮쓪뇪ꆣ쿂쏦틔쫽톧웚췻ꆢ랽닮뗈쫽ퟖ쳘헷캪샽쮵쏷쯼살퓚ퟔ좻뿆톧뫍짧믡뿆톧훐뗃떽쇋뇈뷏맣랺뗄펦퓚뺭볃맜샭뻶닟훐뗄펦폃ꆣ폃,퓚짧믡짺닺뫍짺믮훐웰ퟅ럇뎣훘튪뗄ퟷ폃ꆣ떱샽1ꆡ쒳죋폐튻뇊뷰,뿉춶죫죽룶쿮쒿:랿닺뷱룅싊춳볆폫뺭볃뗄맘쾵뿉틔쮵쫇쾢쾢쿠맘뗄,벸Xꆢ뗘닺Y뫍짌튵Z,웤쫕틦뫍쫐뎡ힴ첬폐맘,죴냑뫵죎뫎튻쿮뺭볃톧뗄퇐뺿ꆢ뻶닟뚼샫늻뾪쯼뗄펦폃,캴살쫐뎡뮮럖캪뫃ꆢ훐ꆢ닮죽룶뗈벶,웤랢짺뗄룅싊샽죧:쪵퇩짨볆ꆢ뛠풪럖컶ꆢ훊솿뿘훆ꆢ돩퇹볬닩ꆢ볛럖뇰캪p1=,p2=,p3=,룹뻝쫐뎡뗷퇐뗄룱뿘훆뗈뚼튪폃떽룅싊춳볆횪쪶ꆣ쪵볹횤쏷,룅싊쟩뿶뿉횪늻춬뗈벶ힴ첬쿂룷훖춶뗄쓪쫕틦(췲춳볆쫇뛔뺭볃톧컊쳢뷸탐솿뗄퇐뺿뗄폐킧릤뻟,캪풪),볻뇭1:뺭볃풤닢뫍뻶닟쳡릩쇋탂뗄쫖뛎ꆣ놾컄춨맽튻킩뻟뇭1ꆡ룷훖춶쓪쫕틦럖늼뇭쳥뗄샽ퟓ쳖싛룅싊춳볆퓚뺭볃맜샭뻶닟ꆢ뺭볃쯰쪧뫃훐닮맀볆ꆢퟮ듳뺭볃샻죳쟳뷢ꆢ뺭볃놣쿕ꆢ뺭볃풤닢뗈벸p1===랿닺113-3룶뺭볃톧컊쳢훐뗄펦폃ꆣ뗘닺64-1짌튵102-21ꆡ퓚뺭볃맜샭뻶닟훐뗄펦폃쟫컊:룃춶헟죧뫎춶뫃?퓚뷸탐뺭볃맜샭뻶닟횮잰,췹췹듦퓚늻좷뚨뗄뷢ꆡ컒쏇쿈뾼달쫽톧웚췻,E(X)=11ꇁ+3쯦믺틲쯘,듓뛸쯹ퟷ뗄뻶닟폐튻뚨뗄럧쿕,횻폐헽ꇁ+(-3)ꇁ=,E(Y)=6ꇁ+4ꇁ좷ꆢ뿆톧뗄뻶닟닅쓜듯떽틔ퟮ킡뗄돉놾믱뗃ퟮ듳뗄+(-1)ꇁ=,E(Z)=10ꇁ+2ꇁ+낲좫놣헏뗄ퟜ쒿뇪,닅쓜뺡뿉쓜뷚풼돉놾ꆣ샻폃룅(-2)ꇁ=,룹뻝쫽톧웚췻뿉횪,춶랿닺뗄[쫕룥죕웚]ꆡ2009-01-05[ퟷ헟볲뷩]ꆡ틗퇞뒺(1974-),얮,뫢퇴쪦랶톧풺쫽톧쾵붲쪦,퇐뺿랽쿲:룅싊춳볆ꆣꆤ89ꆤ
2009쓪4퓂새랻쪦랶톧풺톧놨(ퟔ좻뿆톧냦)뗚9뻭ꆤ뗚2웚욽뻹쫕틦ퟮ듳,뿉쓜톡퓱랿닺,떫춶튲튪뾼싇럧풪,뇪ힼ닮뗄맀볆횵캪풪ꆣ쿕,컒쏇퓙살뾼싇쯼쏇뗄랽닮:D23ꆡ퓚쟳뷢ퟮ듳뺭볃샻죳컊쳢훐뗄펦폃(X)=(11-4)ꇁ+(3-4)ꇁ+(-32-4)ꇁ=죧뫎믱뗃ퟮ듳샻죳쫇짌뷧폀풶ힷ쟳뗄쒿뇪,쯦D2(Y)=()ꇁ+()ꇁ+믺뇤솿몯쫽웚췻뗄펦폃캪듋컊쳢뗄뷢뻶쳡릩쇋탂뗄2()ꇁ=쮼슷ꆣD(Z)=22()ꇁ+()ꇁ+샽3ꆡ쒳릫쮾뺭쿺쒳훖풭쇏,룹뻝샺쪷쇏:헢2()ꇁ=훖풭쇏뗄쫐뎡탨쟳솿X(떥캻:뛖)럾듓(300,500)짏틲캪랽닮폺듳,퓲쫕틦뗄늨뚯듳,듓뛸럧쿕튲뗄뻹퓈럖늼,쎿쫛돶1뛖룃풭쇏,릫쮾뿉믱샻잧듳,쯹틔듓랽닮뾴,춶랿닺뗄럧쿕뇈춶뗘닺뗄럧풪;죴믽톹1뛖,퓲릫쮾쯰쪧잧풪,컊릫쮾펦룃쿕듳뗃뛠,죴쫕틦폫럧쿕ퟛ뫏좨뫢,룃춶헟뮹쫇펦ퟩ횯뛠짙믵풴,뿉쪹웚췻뗄샻죳ퟮ듳?룃톡퓱춶뗘닺캪뫃,쯤좻욽뻹쫕틦짙췲풪,떫럖컶:듋컊쳢뗄뷢뻶쿈쫇붨솢샻죳폫탨쟳솿뗄럧쿕튪킡튻냫틔짏ꆣ몯쫽,좻뫳쟳샻죳뗄웚췻,듓뛸뗃떽샻죳맘폚믵풴뗄2ꆡ퓚뺭볃쯰쪧맀볆훐뗄펦폃몯쫽,ퟮ뫳샻폃쟳벫횵뗄랽램뗃떽듰낸ꆣ뷢ꆡ짨릫쮾ퟩ횯룃믵풴a뛖,퓲쿔좻펦룃폐쯦ퟅ뺭볃붨짨뗄룟쯙랢햹,믰퓖ꆢ뎵믶뗈룷훖틢300ꇜaꇜ500,폖볇Y캪퓚a뛖믵풴뗄쳵볾쿂뗄샻췢쫂맊쯹퓬돉뗄뺭볃쯰쪧돉쏷쿔짏짽뗄쟷쫆,듓뛸죳,퓲샻죳캪탨쟳솿뗄몯쫽,벴Y=g(X),평쳢짨쳵싲놣쿕돉캪룷떥캻벰룶죋럖떣뺭볃쯰쪧뗄튻훖폐킧랽램ꆣ샻폃춳볆횪쪶뿉틔맀볆룷훖틢췢쫂맊랢짺뗄볾횪:떱Xꇝa쪱,퓲듋a뛖믵풴좫늿쫛돶,릲믱샻뿉쓜탔틔벰랢짺뫳떼훂뗄뺭볃쯰쪧듳킡ꆣ쿂쏦틔닎;X<a쪱,퓲쫛돶X뛖(믱샻),쟒뮹폐a쫽맀볆캪샽살쮵쏷쯼퓚헢튻랽쏦뗄펦폃ꆣ-X뛖믽톹(믱샻(a-X)),쯹틔릲믱샻샽(a-X),평듋뗃2ꆡ틑횪쒳닖뿢믵컯퓚뒢님맽돌훐,닖뿢믵컯틲믰퓖뛸쯰쪧뗄뷰뛮럾듓헽첬럖늼N(ꛌ,ꛒ2ꆡꆡꆡꆡXꇝa),뷱Y=g(X)=,쯦믺돩좡8듎믵쯰쇏,뗃떽죧쿂닖뿢믵컯쯰쪧뷰ꆡX<a뛮뇭ꆣ듓뛸뗃뇭12ꆡ닖뿢믵컯쯰쪧뷰뛮뇭E(Y)=ꇒ+ꇞg(x)pX(x)dx=-ꇞꇒ500g(x)dx300200믵컯쯰쪧뷰뛮(풪)1000200030005000듎쫽21411=ꇒa1()dx+ꇒ500a200뷢ꆡ샻폃뻘맀볆램믲ퟮ듳쯆좻맀볆램뿉횪:ꛌ,1ꛒ=2(-a+2900-300)2뗄뻘맀볆솿럖뇰캪200:ꛌ^1=ꇆn1짏쫶볆쯣뇭쏷E(Y)쫇a뗄뛾듎몯쫽,폃춨뎣Xi=X
,ꛒ^2=ꇆn(Xi-X
2),듓뛸룹뻝ni=1ni=1쟳벫횵뗄랽램뿉틔쟳뗃,떱a=450뛖쪱,쓜릻쪹뗃뇭2훐뗄쫽뻝뿉볆쯣돶:웚췻뗄샻죳듯떽ퟮ듳ꆣꛌ^1=(1000ꇁ2+2000ꇁ1+3000ꇁ4+5000ꇁ1)84ꆡ퓚뺭볃풤닢훐뗄펦폃=2625퓚쪵볊뺭펪훐,탭뛠솿횮볤듦퓚쒳훖쏜쟐솪쾵,ꛒ^21=22[(1000-2625)ꇁ2+(2000-2625)+8룹뻝쫽샭춳볆풭샭,뿉틔룹뻝췹쓪쇏믲쫐뎡탅쾢,22(3000-2625)ꇁ4+(5000-2625)]=춨맽뛔짧믡뺭볃쿖쿳횮볤뿍맛듦퓚뗄틲맻맘쾵벰웤ꛒ^=ꆣ뇤뮯쟷쫆뷸탐쿟탔믘맩럖컶풤닢,듓뛸뗃돶캴살뗄듓뛸뗃떽닖뿢믵컯쯰쪧뗄욽뻹맀볆횵캪2625쫽솿ힴ뿶ꆣ쿂쏦틔튻풪쿟탔믘맩럖컶캪샽첽쳖튻쿂ꆤ90ꆤ
뗚9뻭ꆤ뗚2웚틗퇞뒺뗈:룅싊춳볆퓚뺭볃톧훐뗄펦폃2009쓪4퓂쿟탔믘맩럖컶퓚뺭볃풤닢훐뗄펦폃ꆣ놣쿕,퓚튻쓪샯헢킩죋쯀췶뗄룅싊캪,쎿죋쎿샽4ꆡ뫏뷰뗄잿뛈y(ꇁ710Pa)폫뫏뷰훐첼뗄몬쓪뗄춷튻쳬쿲놣쿕릫쮾붻뢶놣쿕럑12풪,쯀췶쪱볒솿x(%)폐맘,캪쇋짺닺잿뛈싺ퟣ폃뮧탨튪뗄뫏쫴뿉틔듓놣쿕릫쮾쇬좡2000풪놣쿕뷰,쟳:(1)놣쿕뷰,퓚튱솶쪱튪뿘훆첼뗄몬솿ꆣ쿖뗷닩쫕벯쇋12ퟩ릫쮾튻쓪훐믱샻늻짙폚10000풪뗄룅싊;(2)놣쿕릫쫽뻝,볻뇭3,쫔붨솢쫊떱뗄쿟탔믘맩쒣탍늢뷸탐볬쮾뿷놾뗄룅싊ꆣ퇩ꆣ죧맻퓚튱솶맽돌훐춨맽뮯퇩뗃횪쇋첼뗄몬솿캪뷢ꆡ짨튻쓪훐쯀췶뗄죋쫽캪X,쯀췶싊캪p=,룹뻝쒣탍풤닢헢슯뫏뷰뗄잿뛈ꆣ,냑뾼싇2500죋퓚튻쓪샯쫇럱쯀췶뾴돉2500뇭3ꆡ뫏뷰룕잿뛈폫첼몬솿뗄쫽뻝뇭훘Bernoulli쫔퇩,퓲탲뫅x(%)y(ꇁ107Pa)탲뫅x(%)y(ꇁ107Pa)np=2500ꇁ=,np(1-p)=2500ꇁꇁ=,놣쿕릫쮾쎿쓪쫕죫캪2500ꇁ12=30000,뢶돶풪,퓲룹뻝훐탄벫쿞뚨샭뗃:뷢ꆡ뗚튻늽(1)쯹쟳룅싊캪:,붨솢쿟탔믘맩쒣탍틑횪튻풪쿟탔믘맩쒣탍캪P(30000-2000Xꇝ10000)=P(0ꇜXꇜ2)y^=a+bx,룹뻝릫쪽벰뇭훐뗄쫽뻝뗃:a=,b=,듓뛸쯹쟳=Pꇜꇜ뗄믘맩쒣탍캪^=+ꆣ뗚뛾늽,볬퇩쿟탔맘쾵뗄쿔훸탔=ꚵ()-ꚵ()=ꚵ()-ꚵ()쿖퓚폃==ꆣt볬퇩램,뺭볆쯣뗃t=,좡쿔훸탔쮮욽ꛁ(2)쯹쟳룅싊캪:=,퓲(10)=,평폚(30000<2000X)=P(X>15)2872>,틲듋퓚쿔훸탔쮮욽ꛁ=쿂믘맩랽닮쫇쿔훸뗄ꆣ=P>뗚죽늽,풤닢=1-ꚵ()ꇖ0ꆣ붫x0=듺죫믘맩쒣탍,퓲뗃떽풤닢횵캪뺭짏쫶볆쯣뿉횪튻룶놣쿕릫쮾뿷놾뗄룅싊벸뫵y^0=+ꇁ=,퓚쿔훸탔쮮욽캪0,헢튲쫇놣쿕릫쮾샖폚뾪햹튵컱뗄튻룶풭틲ꆣꛁ=쿂,뗃y0뗄룅싊캪뗄풤닢쟸볤캪(46.[닎뾼컄쿗]25[1]?쪫쯉,돌틀쏷,쿾쇺.룅싊싛폫쫽샭춳볆뷌돌[M].놱,),벴폐95%뗄냑컕죏캪,첼뗄몬솿캪쪱,뫏뷰뗄잿뛈뷩폚(ꆫ뺩:룟뗈뷌폽돶냦짧,2004.)횮볤ꆣ[2]쇵맰솫.싛룅싊뫍쫽샭춳볆퓚웳튵럧쿕럖컶훐뗄펦폃5ꆡ퓚뺭볃놣쿕컊쳢훐뗄펦폃[J].짌쟰횰튵벼쫵톧풺톧놨,2005,4(2):15-16.쒿잰[3]쯯폱럒.룅싊춳볆퓚짌욷짺닺뫍쿺쫛훐뗄튻킩펦폃[J].,놣쿕컊쳢퓚컒맺쫇튻룶죈뗣컊쳢ꆣ놣쿕릫쮾캪룷웳튵ꆢ룷떥캻뫍룶죋쳡릩쇋룷훖룷퇹뗄놣놣즽쪦톧놨.2003,22(2):51-56.[4]웮뫬맢.잳첸룅싊춳볆퓚뻶닟폅뮯훐뗄펦폃[J].즳퇳쪦쿕놣헏럾컱,죋쏇ퟜ믡풤쯣쒳튻튵컱뛔ퟔ벺뗄샻틦랶룟뗈뿆톧킣톧놨.2005,(5):28-30.폐뛠듳,믡뮳틉놣쿕릫쮾뗄듳솿엢뎥쫇럱믡뿷놾ꆣ[5]쿂쏦틔훐탄벫쿞뚨샭쮵쏷쯼퓚헢튻랽쏦뗄펦폃ꆣproductivity[J].EuropeanEconomicReview,1990,34:355-샽5ꆡ틑횪퓚쒳죋쫙놣쿕릫쮾폐2500룶죋닎볓363.ꆤ91ꆤ
