哈佛商学院MBA教程（下）

80000200400xXXXXnXnniin=++++=∑1231xx=+++++++++++==17151816171614171615181612195121625.()XXffiiiniin===∑∑11XXff=∑∑XfXfiiin=∑∑1().(X)(f)(Xf)20102002212264242560026307803018540321548033103301203,194XXff===∑31941202661,.()XXff=∑∑XXff=∑∑WfXfiii=∑XXff=∑∑XXWii=∑ffffXXfffXnfXnn120======∑∑∑∑:2()XfXf5060551055060706510650708075302,250809085103,4009010095109501007,800XXff===∑∑780010078,()111111111031212XXXXnXHnXXXnXHhh=+++=++=∑:()XnXH==++=∑131101081050071....(/)111223312312311223311XmXmXmXmXmmmmXmmmmmXmXmXmXmmXHnnnHnnniiniiin=++++++++=++++++++===∑∑XmmXXfXfXXffXmXfH=====∑∑∑∑∑∑()XhXmimXhiii=====∑∑141145000012194102,,.()/XmmX3510,0002864020,0005004515,000333505,00010050,0001,219XXXXXGnnn==∏12XGlog(loglogloglog)logXnXxXXnXGnn=++++=-∑11121ΛXfiXfXfXfXfGikkk==∑1112233=+n12()5060246070487080105809060901002711012021100110121201303300f∑==23002150∏XnMLdddi0112=++×MUdddi0212=-+×ADXXN..=-∑σ22=-∑()XXnσXσ=-∑()XXn2σiXi()XX()XXi-2Xi211130012,769212186414,64131130012,76941141112,99651130012,76961141112,99671152413,225810674911,23691112412,321101103912,1001,1300132127,822XXXXXnXXnXXnXXXXnii==-=-===-==-=-+∑∑∑∑∑113010113213210132132363222222,()()().()..()()[()]σσ=-+=-+=-∑∑∑∑XnXXnXXnXXXnX222222222()()()()σσ22222=-⎡⎣⎢⎢⎤⎦⎥⎥=-⎡⎣⎢⎢⎤⎦⎥⎥∑∑∑∑XnXnXnXnσσ222=-=-∑∑∑∑()()XXffXXffiiXσVADXVXAD....=×=×100%100%σσX=⎧⎨⎩10XPxxxpppkk1212ΛΛΛΛΛΛΛΛ:()()()FxPXxpxxixxi===∑xixiP(X=xi)011/50122/50244/50333/50466/50588/5061010/50777/50855/50933/501011/50501EXxPXxii()()===∑μσDXE{[XEX()()]}=-=22σσ=DX()DXEXxPXxii()[()]()()=-=-=∑μμ22DXEXEX()()[()]=-22DXE{[XEXE{XXEXEXEXEX()()]}()[()]}()[()]=-=-+=-222222μσμ===×+×+×+×+×+×+×+×+×+×+×==-==-×+-×+-×+-∑∑xPxxxPXxiiiii010222220150125024503350465058508105077508550935010150538053815015382502538450().()()(.)(.)(.)(.)(.)(5.)(.)(.)(8.)(.)(.).353835045386505388506538105075387505385509538350105381505195622222222-×+-×+-×+-×+-×+-×+-×+-×=PXaabPXbab{},{}==+==+10PXpppPXp{}((){}====-10101AAAAAAAAA123123123P2{}()()()()()()()()=++=-+-+-=-=-PAAAPAAAPAAAppppppppCpp1231231232222322111311PXkCpqknnkknk()(,,,,)===-012ΛPxkkkek{}!(,,,,)===-λλλ0120ΛΛPXkCCCkMnmkNMnkNn()(,,,min(,))===--012Λfx01:()()():()()xdxfxFxFxfxdxx-∞∞-∞∫∫==PaxbfxdxFbFaab()()()()≤≤==-∫Exfxdxx()()-∞∞∫DXE{[XEXxEXfxdx()()]}[()]()=-==-∞∞∫22fxbaaxb()=-≤≤←⎧⎨⎪⎪⎩⎪⎪⎫⎬⎪⎪⎭⎪⎪1010ab+2()ba-212Fxxaxabaaxb()=≤--⎧⎨⎪⎪⎩⎪⎪0fxexxx()()=≥⎧⎨⎪⎩⎪-λλλ0000λFxxexx()=≤-⎧⎨⎩-0010λfxeXx()()()=-∞+∞--12222πσμσσσf()μπσ=12f()μπσ=12σσFxedxxx()()=---∞∫12222πσμσfxex()=-1222πFXXexdxx()()==--∞∫ϕπ1222σxxμxxσx-2σx-2σxσσ12σ22xx12-σσ121221nn+ppn()1-YEYXx==()0()YXx=0EYXx()=1YEYXx==()YfxEYXxrlxyllxynxyxnxynyxxyyiiiiiiii==---∑∑∑∑∑∑∑1112222()()[()][()]bllxyxx=rblllxxxxyy=Frrn=--2212()ySSyyynyiiniin=-===-∑∑()2111SSyyei2in=∑1SSyyRi2inReiiniinRyyiixxxySSSSSSyyyySSlyyabxabxbxxblbl===∑∑∑∑∑∑=+-=+-==-=+--=-==1212122222,:(∃)()):(∃∃)()()SSSSRSSSSblllllrSSrSSrlRxyyyxy2xxyy2R22yySSSSSSSSlryyl1reeRyyl2gg2rSSSS12Ryyi2∑yyyabx)1i2∑∑∃yyi2∑FSSSSnRe=-//12FSSSSnrlnrlrrnReyyyy=-=--=--//()()()1221222222∃yab∃yabx00∃y0∃yiSyynyxii=--∑(∃)(5)22Syxyaybxyniiii=---∑∑∑∑226()∃()S()()∃()S()()ytnnxxxxyytnnxxxxttayxiaxyia0202200200221121122--++--≤≤+-++--∑∃ybbxbxi011i22iyinbbxxbxxybxbxbxxxybxbxxbx01i1i22i2ii01i11i222i1i1ii02i12i1i22i2∃ybbxbxbx0112233ynbbxbxbxxybxbxbxxbxxxybxbxxbxbxxxybxbxxbxxbx011223310112212313202121222323303131232332∃ybbxbxbx01l22mmynbbxbxbxybxbxbx01122mm0112mmxbxxxybxbxxbxxbxmmmmmm11212011222+=++++ΜΜΛΛSyynmiiin=---=∑(∃)121CCjjojjL-1L-1Llllllllllllxxxxjijmmmmmmmijijitijttn=⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥==--==∑111212122212112ΛΛΛΛΛΛΛΛΛΛΛΛΛΛΛΛΜΜΛΛΛΛΛΛΜΜΛΛΛΛΛΛΛΛΛΛ()(),,,xixnjxjttn==∑11xjxnxjjttn==∑11tbscjmjjjj==12,,,ΛΛta2ttja2∃`yabx=lg∃lglg∃'lg∃,'lg,'lgyaxbyyaabb=+===∃'y'a'bx∃yabxcxdx23xxxxxx12233∃yabxcxdx23ξη19.0012.001.583GNPQPTYPPPdsce=fϑϑ0015050502150751003300100150440010010054809680654090607580834086107630961068030105805830MRTS/LdN/dlLNLMPNMPLN’””’’RC1rr=R-CC()()()1.2.3.4.5.6.7.8.9.10()()()()510155101520PUVA()BC30252015101312.54307520254035210.59012540155434.52.02.51207590302510019027534020,00021,00026500ABC500PUV2500QCPVE=-QCPC12=+-SSSSP(S)P(S)P(S)P(S)AAΜAΜAVVVVVVVVSAASimijjn=∑=112(,,,)ΛQ011xxin11=∑gxgxgxgxiinnin()()()()=+++=∑1221ΛΛfQMaxgxxniiiin()()()=≥=∑021ΛΛgXfQXnnnn()()+--1fQMaxXQgXfnnnnn()[())()]=≤≤≤+-0031ΛΛfQgQ411fQMaxXQgXfQx2222120()[()()(5)]=≤≤+-ΛΛgfQ-xgfQ0g1fQ-1g2fQ-2gQOg2fQxfQ22i2211122221222xfxx012ΜΜfQMaxXQgXfQxn3063333()[()()()]=≤≤+-ΛΛ(Q)Ag(Q)Bg(Q)Cg(Q)12345153678901001635709211020408090110fMaxgfgf22121101151016()()()()()=+=+=⎧⎨⎩⎫⎬⎭fMaxgfgfgf22121211023611312035()()()()()()()=+=+=+=⎧⎨⎪⎩⎪⎫⎬⎪⎭⎪fMaxgfgfgfgf22121212130378123121523070()()()()()()()()()=+=+=+=+=⎧⎨⎪⎪⎩⎪⎪⎫⎬⎪⎪⎭⎪⎪fMaxgfgfgfgfgf23132323232404901394227131854092()()()()()()()()()()()=+=+=+=+=+=⎧⎨⎪⎪⎪⎩⎪⎪⎪⎫⎬⎪⎪⎪⎭⎪⎪⎪fMaxgfgfgfgfgfgf23132323232320100141062311332106411070110(5)()(5)()()()()()()()()(5)()=+=+=+=+=+=+=⎧⎨⎪⎪⎪⎩⎪⎪⎪⎫⎬⎪⎪⎪⎭⎪⎪⎪fMaxgfgf33232101161020()()()()()=+=+=⎧⎨⎩⎫⎬⎭fMaxgfgfgf33232322013610362040()()()()()()()=+=+=+=⎧⎨⎪⎩⎪⎫⎬⎪⎭⎪fMaxgfgfgfgf33232323230378125621562080()()()()()()()()()=+=+=+=+=⎧⎨⎪⎪⎩⎪⎪⎫⎬⎪⎪⎭⎪⎪fMaxgfgfgfgfgf33232323232404941398227631964090()()()()()()()()()()()=