周概容版概率课后习题答案

《周概容版概率课后习题答案》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

⚪1ᐸᭆ᳛⚪(A)1.6Ꮇᢇ100ᖪᨵ.4ᔠ.᪵ᦈ!"4#Ꮇ᝞%&ᔠ#ᑣ(ᦈ)ᢇ*#ᔲᑣ,ᦈ#-)ᢇ*.,ᦈḄᭆ᳛p.1-⊤45"Ḅ4ᔠḄᦪ#ᑣp=Pv>18=1-Pv=08C4=1;n1—0.8472=0.1528.41.7!0,1,2,…JOF11Gᦪ"HIG#-JᑡḄᭆ᳛LA[=OIGᦪᨬᜧḄR58SA?LOIGᦪᜧUஹFUWXU5ḄᔜG8;4=OIGᦪ[GᜧU5,GXU78.!11Gᦪ"HIG#\ᐳᨵ=165_`"a#ᓽ\ᐳᨵGcd#ᐸᨵᑭU4Ḅ"aᨵCS=10_(IGᦪᨬᜧḄR5,ᙠXU5Ḅ5Gᦪ5"[GᨵCS=10_`"a)SᨵᑭUᓰḄ"aᨵ5x5=20_(ᙠXU5Ḅ5Gᦪ5"G#ᙠᜧU5Ḅ5Gᦪ5"G#ᨵ5x5=25_`"a)SᨵᑭUAḄ"aᨵ5*CS=70_(ᙠXU5Ḅ5Gᦪ5"G#ᙠᜧU5Ḅ5Gᦪ5"[G).U3R#ᨬmnio2550P(AJ=—=0.06,P(A)=—=0.15,P(A)=—=0.30,1651651651.10!0,1,…,9#5"4Gᦪs(ᐕuvw)᣸ᡂᑡ#z{ា}~ᡂGᦪ.-JᑡḄᭆ᳛L4=O4Gᦪs[[F8;A?=OᦪR᜻ᦪ8;43=O6H8;A,=O6ា}H8.ὃ⇋\A=O0,1“,98Ḅ஻=4᪵.cdḄ\ᦪ"=9x10'=9000L•ᦪs(&0)ᨵ9_⌱#ᐸIᦪsᐳᨵ1()3_⌱.ᑖ1N*(k=l,2,…⊤4ᡠcdḄGᦪ.(1)M=9x9x8x7=4536S(2)-2=9x102x5=4500Lᦪsᨵ9WIᨬmᦪsᨵ5_ஹ¡[ᦪsᐳᨵ0_⌱;(3)=9x1O'-8x9ஹ=3168,ᓽcdḄ\ᦪN¢£Ḅ¤¥A=O6H8ᡠcdḄGᦪS(4)N=¦+3x8x9?=2673L¨ᨵᦪR6Ḅᐳᨵ9?_©~#6¨Hᙠ2,3ᡈ4ᦪ«Ḅ©4~ᔜᨵ8x92_SUR#ᡠ-ᭆ᳛&NP(AJ=¬=0.504S44)=~N=0.500SP(4)==0.352S▲)=%0.297.N

11.13Ꮇᵯ°±ṹ&³ᦪ(ᦪ&0),-4=Oᵯ°±ṹ0ᡈ98W&=Oᵯ°±ṹ098Ḅᭆ᳛.µ¶L·=Oᵯ°±ṹ08,¸=Oᵯ°±ṹ98,4=·+89=Oᵯ°±ṹ0ᡈ98,A=B-B=B-BB.᧕º29o90998297g8XP(B0)=-----7,P(BJ=-----P(BB)=----------°9xl079xl07099xl07(1)ᵫ¾a¿À#ÁºPভ=P(B0+BJ=P(B0)+P(BJ-P(BB)09(2)âa¿À#ÁºQQ7xP(4)=P(Å_3°5)=P(Ç)2Çao.2387.71.15ÉÊᭆ᳛P(A)=p,Ë(8)=%Ë(A8)=r.ᑖ-JᑡᔜḄᭆ᳛LA+B,AB,X+F,Ð,4(4+8).ᵫÑÒḄឋÔ#᧕ºP(A+B)=i-P(AB)=l-rP(AB)=l-P(AB)=l-r,fP(AB)=1-P(A+B)=1-[P(A)+P(B)-P(AB)]=1-[p+-4P(A+B)=l-P(A+B)=l-[p+(7-r],P(A[A+B])=P(A+AB)=P(A)=p.1.18Ꮇ×ᨵGᳫ#¨Ê⍝RÚᳫÛRÜᳫ.ᙠÝGÚᳫ¶×#ᯠm!×"HGᳫ#z{RÚᳫ.-×ßᩭRÚᳫḄᭆ᳛a.µ¶LA=O"HḄRÚᳫ8,%=O×ßᩭRÚᳫ8,“2=O×ßᩭRÜᳫ8,ᑣ#42᪀ᡂâᐰä#åæË(ᵨ)=Ë(42)=06.ᵫᩩÊP(A\H)=\,P(A\H)=0.5.l2ᵫéêë¿À#ᨵP(஻JË(A|”J2a=P(HJA)=P(H)P(A\H)+P(H)P(A\H)3ll221.19ᙠïðᵯñò(óôᙢö〈ò±0W1,ᐸ஺ᓰ60%,Ð1ᓰ40%.ᵫUùᙠ¦᡾#ö〈ò±0(ᦈò±ÁûR0#1WX(üýò±)#ᭆ᳛þÿ0.70,0.100.20〈1ᦈ0,1x,ᭆ᳛0.85,0.050.10.ᦈᑮxᨬ!"ᡂ஺%1?'()*+,“0={〈0},/={〈1},4={ᦈA}(k=0,1/),ᑣ8(“0)=0.6,P(H1)=0.4P(A\H)=O.7O,P(4|/)=0.10,P(4|%)=0.20ooP(.IM)=0.05,P(A|HI)=0.85,P(AJH)=O.1O.1ᵫCDEFGHᨵ

2P(H1A,)=----------.....................=0.750P(H0)P(A//)+P(a)P(A"HJP□ভ=1-P("oভ=0.25..QRST⊤VHᙠᦈᑮx"ᡂ0X"ᡂ1!.1.21ᎷZ[ᔆ]^8Ḅ`abᘤHdᭆ᳛0.7defᔆdᭆ᳛0.30◤)[i)jklHmkldᭆ᳛0.90dfᔆ.Hdᭆ᳛0.10opᔠrspfᔆ.tᙠuᔆᙠ^8ᩩ+woḄxyzH{^8|20abᘤ.}ᨬ~20abᘤ(1)fᔆḄᭆ᳛(2)apfᔆḄᭆ᳛.'bᘤḄyḄ.Z/=bᘤ◤⌕kl,"2=bᘤp◤⌕klH4=bᘤdfᔆ.ᵫᩩ+P(”J=0.30,P()=0.70,P(A|"J=0.80,P(A\H)=1.2(1)10abᘤfᔆḄᭆ᳛%=P(A)=()(A□)+P(H)P(A\H)22=0.30x0.80+0.70=0.94஺=☜=0.94ᨌ0.5386.(2)——10ᑖpfᔆḄaᦪHᓽ10ᑭl¡“ᡂ¢(pfᔆ)”Ḅᦪ.ᵫপᡂ¢Ḅᭆ᳛p=0.06.᧕¦H10aapfᔆḄᭆ᳛P=Pv>2"=\-Pv=0"-P[v=1=1-O.9410-10x0.94°x0.06=0.1175.1.23ZA,B©ª*+H«V,(1)¬*+A8Au8,ᑣP(A)=OᡈP(8)=l(2)¬*+ABp±HᑣA5²ᨵ[³0ᭆ᳛*+.«V(1)ᵫ´AuB,¦P(AB)=P(A)P(B),P(AB)=P(4),P(A)=P(A)P(B).µ¶H¬P(A)HO,ᑣ(8)=1¬(8)*0,P(A)=O.(2)¸´*+A8,ᵫ´¹º»p±H¦P(A)P(B)=P(AB)=O,µ¶Hᭆ᳛P(A)(8)ᨵ[³¼´0.(B)[ஹᓫ⚗⌱Á⚪1.25ᵬஹijÅᳫÇ)jXÈHᎷZᨵÉÊḄSË,ᵬÌHÄÌÍÎËHὃ⇋*+A=ᵬÌÄÑ,CÒ(A)ᵨ=ᵬÑ»ÄÌ.(B)ᵬÄÎË.(C)4=ᵬÌᡈÎË.(D)Ö=ÄÌᡈÎË.[]

3ᑖ᪆Ú(D).Û“ᵬஹijÅᳫÇXÈ”ÜÝÞl¡E,ᐸàá*+âa=q,ᵨ,ᵯ,ᐸa=ᵬÌ,#=ÄÌ,ä=ÎË.*+A=ᵬÌÄÑ=å,µ¶•=ᱝè,ᓽé⊤ê“^=ÄÌᡈÎË”.´(D)ëì⌱⚗.íV⚪*+B3,B&dîïàá*+ᑖð⊤ê,B[=a>,B=4=-2┯Ḅ⌱⚗(A),A8=0,ᑣ%,BAB%CD.(B),AB#0,ᑣF,B3ABCD.(C),4?=0,ᑣF,63ABCD.(D),ABH0,ᑣF,8GH%CD.[]ᑖ᪆MN⌱(D).OPᵨR⌱S7HTᔠ⚪W⌕YḄ⌱⚗᝞Zᵨ᣸◀Sᑣ◤⌕*ᐸ>_`⌱⚗ᑖab
.(1)R⌱S*+⌱⚗(D)D᧕b
.AH0,ᓰH0,A=eᑣF=8.ᦑAg=^=A*0.ᯠF,B!ᯠCDjAB=B^0,#$klmnᦑ(D)7o⚪WᡠᢣḄ┯⌱⚗MN⌱(D).(2)᣸◀S4◤brs(A),(B),(C)ABᡂ'ᓽ%Tᔠ⚪9Ḅ┯⌱⚗.᝞,AuBvw*'ᓽ8=ᐘᑣ48=0,3vw*'#$FuW%CDᦑ⌱⚗(A)ᡂ'A8W0A+8W0,yzᎷ᝞ὡ%CDjAB=0,ᑣA+B=AB=0=f2,|eA+8W0mnA}~g3CD⌱⚗(B)ᡂ'A,8%CDA8=0A+஺yz,F,8%CD8=0,ᑣA+==0,|eA+8H0mnA},83CD⌱⚗(C)ᡂ'.

4+(D)Tᔠ⚪9Ḅ⌕YḄ67⌱⚗.1.28*+89_A,8,C,;ᑡᔜ67Ḅ(A)AB=A+B.(B)A+B=A+AB.(C)(A+6)—A=8.(D)A+5C^AC+BC.[]ᑖ᪆MN⌱(B).N⚪PᵨR⌱S.(1)R⌱SᵫḄuឋA}A+B=A+(B-AB)=A+(n-A)B=A+AB.+(B)67⌱⚗.(2)᣸◀S*+⌱⚗(A),#$⌱⚗(A)┯*+⌱⚗(C),(A+8)-A!ᯠ+“8A%“ᓽ8—A=8—A8,#(4⌕A3%%AB)⌱⚗(CJ•¤%ᡂ'ᨬ)*+⌱⚗(D),#wḄ*Ꮤ0¥A+BC^ABC.ᡠ¦⌱⚗(D)G¤%ᡂ'.+4ᨵ(B)67⌱⚗.1.29A,8uC89_ᑣ;ᑡ⌱⚗>67⌱⚗(A),A+C=8+C,ᑣA=8(B),A—C=8—C,ᑣA=8.(C),FC=BC,ᑣX=B(D),48=ª7=0,ᑣ=8.[]ᑖ᪆MN⌱(D).N⚪OᵨR⌱S#wR⌱⚗(A),(B),(C)s!%ᡂ'.(1)R⌱SᵫḄ*Ꮤ0A}AB—A+B=0—.ᵫA+B=0AB=0,A}AuBvw*'ᓽF=8.+(D)67⌱⚗.(2)᣸◀Swrs®_`⌱⚗¯%ᡂ'4◤ᑖab
.ᵫ+:89᝞A^B,C=Q±ᯠᑣA+C=8+C=஺A-C=B-C=0,AW8,³⚪(A)u(B)%ᡂ'A#8,C=0,ᑣAC=8CAwB,³⚪(C)%ᡂ'.+(D)67⌱⚗.rsN⚪Ḅ¶Z
᧜1ḄeᦪḄḄ%¹ºᜐ.1.30*+89A,B,C,,A+BnC,ᑣ(A)A+BC.(B)ABC.(C)A+B^C.(D)AB^C.[]ᑖ᪆MN⌱(C).½⚪PᵨR⌱S.(1)R⌱S#wᵫA+8nC,A}A+8U3,ᡠ¦(C)67⌱⚗.

5(2)᣸◀SD᧕¾s⌱⚗(A),(B)u(D)%ᡂ'.oA=8,ᵫᩩ=A+8nC,¥A+B=AoC,AB=A+B=AaC,#$⌱⚗(A)u(D)¯%ᡂ'ᐸÀᵫᩩA+B=)C,A}ABA+B,ᡠ¦⌱⚗(B)%ᡂ'.+(C)67⌱⚗.rsN⚪A¦ᵨᭆ᳛ḄÃÄ⊤Æwj*+89A,8,C,,A+ᑣ(A)P(A+B)>P(C).(B)P(AB)>P(C).(C)P{A+B)1>.(1)Ï஻ÑÒÓÔÕ(Öw×ØÎᦪ(2)ÏF(x)×ØÔYÕ{|X|1>.(2)ᵫ+ᑖÎᦪÕ(x)×ØÎᦪA}^.iarcsmi-l-larcsmZl^xlarcsini^,27122ᐔ2ᐔ232.6YÞᦪC,ᎷXḄᭆ᳛ᑖwCP{X=Z}=L=1,2,

6Ùᵫª▲çᦪḄYuèᨵeecC1/21=/P{X=k}=——=Cx—:—'—,C=l.éé2«1-1/22.7ÚG⚩⁐ìíîÀ¦X⊤ïîÀíḄᨬðñᦪYXḄᭆ᳛ᑖ.ÙÚG⚩⁐ìíîÀᨵ36`ABò½j/2={0",j=l,2,…,6},Xᨵ1,2,…,6`ABÓ.ᙠ36`ò½>ᨵᑭ+{X=l}Ḅ11`j(1,1),஺,2),…,(1,6),(2,1),(3,1),…,(6,1)ᨵᑭ+{X=2}Ḅ9`j(2,2),(2,3),…,(2,6),(3,2),(4,2),…,(6,2),…ᨵᑭ+{X=6}4ᨵ1`j(6,6).ᵫ$᧕}XḄᭆ᳛ᑖw:'123456ஹXõ1197531•<363636363636>2.8ö÷>ᨵ7`éᳫ3`ùᳫúÀ>8ÑGᳫ%ûüý.(1)Y4ÀþᳫùᳫÀᦪXḄᭆ᳛ᑖ(2)þᳫRᑮ✌
ᳫᳫᦪyḄᭆ᳛ᑖ.পXᨵ0,1,2,34WBᑖ!⊤#ᳫ$ᳫᑣ&'“4ᳫ”)*+“-7W3B”Ḅ./Ḅ4012᪵ᐸ5678.ᦪC9஺=210,ᐸ;ᨵᑭ+{X=k}(>=0,1,2,3)Ḅ5678ᦪ9C9C?@,BCDED£G43P[X=k}=(%=0,1,2,3),ᡈ(0123ஹ9123ஹX135105637=\_j_31To<2102102W210><6230>(2)yJᯠᨵ1,2,3,44?W*B”ᑖ!⊤#L%(k=1,2,3,4)ᑮᳫ$ᳫᑣ“012ᳫNᑮ✌
ᳫ”)*+“P-7ᳫ3$ᳫḄ./Ḅ4012᪵”ᐸ5678.ᦪP9=10x9x8x7=120.᧕R3x728P{Y=2}=12010x93x2x773x2xlx71P{Y=3}=P{Y=4}=10x9x812010x9x8x7nori234ஹy5842871T20<120120120>2.11SXTUVWᑖXYZP{X=l}=P{X=2}P{X=4}.fX⊤#[\ḄG⚓Eᓺᑵ┯aḄᦪbc=1,2,3,4)⊤#[\ḄLk⚓Eᓺᑵ┯aḄᦪᵫᩩ8ZX=1,2,3,4)TUgGVWᑖhZᑖiᦪjkl+ᩩ89

7P{X=1}=m{X=2},/16஽=+6G”.+o2=2.ᵫ+X«(k=1,2,3,4)Jᯠ)pqrBCP{X1=O,X=0,X=0,X=0}234=P{X=0}P{X=0}P{X=0}P{X=0}t234=s)4=6Gt0.0003.2.14SXTUuv2,5EḄᙳᒴᑖyXz{3qr|};~ᨵ2Ḅ|}ᜧ+3Ḅᭆ᳛a.1᧕R78A={X>3}Ḅᭆ᳛P(A)=P{X>3}=f1dx=g.SA={X«>3},ᑣᵫᩩ8ZA14,4)pqrXm(A«)=2/3(l,2,3).788={yXḄ3qr|};~Ḅ|}ᜧ+3},ᑣ={yXḄ3qr|};|}0ᜧ+3ᡈាGᜧ+3}?B=AAA+AAA+4A2&+4@&?2a=P(B)=\-P(B)=i-p(AAA)+P(AW4)+p(AaA)+P(AM)16,720=1----H-----=1------=—272727272S3qr&'784=9>3}
ḄᦪᑣTUiᦪ(3,p)Ḅ⚗ᑖᐸ;0=2/3.BCa=P(B)=P{Y=2}+P{Y=3}4820=3p“l—p)+p3=G+—=—927272.22SXTU-1,2EḄᙳᒴᑖ,yḄᑖᐸ;若<0-1,若y=ᵫ+xTU-1,2EḄᙳᒴᑖZḄᭆ᳛ᑖP{Y=-1)=P{X<0}=P{-10}=P{02.24yᙊᱏḄNz{}}Rᙠ5,6Eᙳᒴᑖᙊ☢SḄᦪg(s).ᙊ☢SoN}RḄoḄᦪ9ᵫ+Rᙠ5,6E\ᙠ5,6᜜R=0,BCNRᙊ☢⊤#

8-7i/?2,RE[5,6],s=<40,Ae[5,6].᧕Rᙊ☢SḄ¢+uv6.25ᐔ,9ᐔIᐸᑖᦪG(S)=P{S4S}=P{?TTR24s}=P‘R<ᵨ¥ᵫ+ᙊ☢SḄ¢+uv6.25ᐔ,9ᐔ¦,Ry+sc6.25ᐔ,9ᐔ¦,ᨵg(s)=§G(s)=1l~ji~4_1as2V4?7iVirs)+oᙊ☢SḄᦪ}—,6.25ᐔ($§9ᐔ,g(S)=,V71S0,0ᯠ.2.26Sᵯ«¬/oGᙠ9A11Avᙳᒴᑖ?YZCᵯ«®¯2஺Ḅᵯ°±²ὑḄ´᳛µ=2¶µḄᭆ᳛.ᵯ«/ᙠuv(9,11)Eᙳᒴᑖᐸᭆ᳛/=|rG·)W0,x¸(9,11).ᵫ+y=2/(9

9ᑖ᪆ÏÐ⌱(A).BÑÒ⌱⚗ÓÔÕJᦑ×ᵨN⌱.(1)N⌱ᵫ+ᭆ᳛oᦪᦑ(A)oÑÒ⌱⚗.(2)᣸◀ÚÕ⌱⚗(B)(C)(D)oÏ᣸◀Ḅ┯a⌱⚗Û◤ᑖ!Ý
¿Þ.7ßEàZᭆ᳛-áhâo»¼ᦪÞ᝞ᙳᒴஹᢣᦪᑖ0o»¼ᦪᦑ⌱⚗(B)┯a?ᙳᒴஹᢣᦪᑖ0Íᦑ⌱⚗(C)┯a?ᭆ᳛0å+0,æohâ0ᜧ+1?Þ᝞uv[0,0.5]EḄᙳᒴஹiᦪ2Ḅᢣᦪᑖᐸᨬᜧᜧ+1,*èéᐙᑖå±Ñ᝱Ḅᨬᜧìᜧ+1.+o⌱⚗(B)(C)(D)oÏ᣸◀Ḅ┯a⌱⚗.2.28SXNQ1),ᐸᭆ᳛“X),ᑖᦪm(x),ᑣ(A)/(%)=/(-%).(B)F(0)=l-F(0).(C)F(x)=F(-x).(D)m(1)=1—Fপ.[]ᑖ᪆Ïí(D).পN⌱By+Xm(1)=0.5,ᦑm(1)=0.5=1—0.5=]_m(1).U(D)oÑÒ⌱⚗.(2)᣸◀ᭆ᳛/(x)Jᯠ0oᏔᦪᦑ⌱⚗(A)┯a?⌱⚗(B)ᡂr*Xò*/(0)=0.5,ᯠy+XN(l,l)Jᯠm(0)#0.5,ᦑ⌱⚗(B)ìo┯a⌱⚗.ᨬóÞ᝞F(l)=0.5>F(—1),ᦑ⌱⚗(C)ìo┯a⌱⚗.+o⌱⚗(A)(B)(C)oÏ᣸◀Ḅ┯a⌱⚗.2.29SXTUᢣᦪᑖY=min{X,2},ᑣVḄᑖᦪ(A)o»¼ᦪ.(B)~ᨵvôõ.(C)o▤÷ᦪ.(D)ាᨵGvôõ.[]ᑖ᪆Ïí(D).7ßEBXḄᑖᦪF(x)=0(x<0),F(x)=1-(x>0)o»¼ᦪ.SG(y)o=min{X,2}ḄᑖᦪᑣG(y)=P{Æ}[7ù.[1”2.BG(2)=1úফ=1—e-2—41,ᡠG(y)ᙠy=2ᜐាᨵGvôõ.2.30SF(x),F(x)oḄᑖᦪfi(x),/(x)o)ÏḄᭆ᳛ᑣx22(A)F|(x)+F2(x)oᑖᦪ.(B)F[(x)F2(x)oᑖᦪ.(C)þ(x)+/2(x)oᭆ᳛.(D)þ(x)%(x)oᭆ᳛.[]ᑖ᪆ÏÐ⌱(B).Ð⚪×ᵨN⌱ÿ
ᵨ᣸◀.(1)⌱F(x)=F](x)&(x)◤E(x)ᐹᨵᑖᦪḄᩩឋ.ᑖᦪᨴ(x)5(x)Ḅឋ04!(x)41"ᓫ$%&Ḅ'()ᦪ*+,F(-8)=0,/(+8)=1,-.!(x)=—(x)%(x)/0"1ᑖᦪ-.(B)"23⌱⚗.

10(2)᣸◀8᧕:(A),(C)(D)%ᡂ@A᝞F(+oo)+F(+oo)=2,ᦑ(x)+F(x)%"ᑖᦪ}12-.⌱⚗(A)┯JKᵫMN"(P+—(ᑗ*=2,T(X)+/2(X)%"ᭆ᳛YZ-.⌱⚗(C)┯JKᨬ\T(X)"᪗^2᝱YZ`/2(X)"abcḄᙳᒴᑖYZᑣgT(ᑘT(X)*=-7=e2dxᱏ1,-.f\(x)o(x)%"ᭆ᳛YZM"ᨵ(B)"23⌱⚗•2.31stuvY=aX+b(a^0)wstuvXxyz{|}ᑖ᝞~Xxy(A)⚗ᑖ.(B)ᑖ.(C)2᝱ᑖ.(D)ᢣᦪᑖ.[]⌱(C).⚪ᵨ⌱-2᝱ᑖstuvḄឋᦪᯠxy2᝱ᑖ"Ḅপ⌱.stuvXxy2᝱ᑖN(஻,er?),ᐸᭆ᳛YZ᜛(x),p(y)⊤stuvY=aX+b(a^0)Ḅᭆ᳛YZ.-awO,ᡠᦪ¤=஺¦+/¤ᨵ§{¨ᦪx=/z(y)=±^,—=/z(},)=—;adya®/i(y)"(y)°ᐭstuvḄᦪḄYZ²³(2.8),µ¶=aX+஺Ḅᭆ᳛YZp(y)=(p(h(y))\h,(y)\11gy—Z?T]1y/2iia2baJJ|a|=[)-m஻+Ẇ.ᵫ.Y=aX+b-N(aju+b,a2a2),M"⌱⚗(C)23.(2)᣸◀.¾M(A)(B),ᵫMy=aX+b{¿%ÀÁᯠᦪÂᡠ{¿%xy⚗ᑖᑖ.¾M(D),ᎷXxyÄᦪÅḄᢣᦪᑖᐸᭆ᳛YZÈx>0,/&)=0,(x<0KY^aX+bḄᭆ᳛YZf(h(y))\h'(y)\,(y>b,p(y)=0,Èyb,0AÈy

11┯J⌱⚗ᨵ(C)"23⌱⚗.Ó⚪3stᔣvÕᐸᭆ᳛ᑖÓ⚪Ö(A)3.2!{X20,y20}=3/7,P{X>0}=P{7>0}=4/7,ÚP{min[X,Y]20}.ÝÞßàA={XN0},5={7>0},âij{min[X,Y]20}={X20}+»20}=A+8.ᩩßà43P(A)=P(B)={,P(AB)=-K77-.ᵫå²³P{min[X,y]>0}=P[A+B)=!(A)+P(B)-P(AB)=*3.3ᎷstuvUᙠab[-2,2]xyᙳᒴᑖstuv¶_é1,ÈUW-1,y_(U41,=|1,ÈU>-1K=11,ÈU>1.ÚxyḄὶᔠᭆ᳛ᑖ.stᔣv(x,y)ᨵ(-1,-1),(-U),(1,1)í41îÂp{x=-i,y=-i}=P{U<-\,ui}=p(0)=o,p{x=i,y=—i}=p{u>—i,u«i}=!{_i-l,U>\}=P{U>1}=^.M"xyḄὶᔠᭆ᳛ᑖf(-i-i)(-14)(i,-i)(i,i»(x,y)~iii.nI424)3.6stuvXyḄὶᔠYZ,,ஹ—|X2+—|>È0cxe1,0/}K(3)Úᩩßᭆ᳛!ý>0.5IX<0.5}.(1)᧕þxe(0,1)ÿ(x)=00

12=஻%ᵫ:=ᯠ+.6z/.oஹAy=—(2x~+x),—(2x2+x),0cx<1,(x)=170,ᯠ.ফ!“xᜧy”Ḅᭆ᳛&{X>y}=]j7(x,y)dxdy=([drf2xy].67x>y(3)ᩩ!ᭆ᳛ᐸ)P{X<0.5}=/5(x)dx=|f(2x2+x)&=£P{X<0.5,y>l}=g*drfJ++112,-e*஺1233.7Ꮇ56789X:;ᔠ=>?BᐔCsin(x+y),(0(y|X=x)de0

13(y|X=x)=1^F(x)‘m@+220ᑖ<=<(sinx+cosx)/22.0,ᯠ2ᵪ0“J,=5sinx+cosx20,ᯠ.3.9wG67ᔣ9(X,y)Ḅᭆ᳛=>?fe"\0£(x):஺')(2)Ex+yᜧ1Ḅᭆ᳛.O1)6789x:yḄᭆ᳛=>(x):2(y),/(x,y)ḄTU=>;^e~vdy,x>0,^e-A,x>0,f^x)=f஻x,y)dy=0,x<0,0,(x<0.᪵R6789yḄᭆ᳛=>N-oCye~y>y>0,f(x,y)dx=-J-CO0,(y<0.(2)X+Yᜧ1Ḅᭆ᳛P[X+Y<1}=jjf(x,y)dxdyx+ySl=£fe-ydy=l+e-1-2e-,2ᐸ)ᑖ,Ḅ▢ᑖ.3.1156789x:yḄὶᔠ=>?2ᓱ>,x>0,y>0,f(x,y)=-0,x40ᡈy40.E6789x:yḄὶᔠᑖᦪ:ᭆ᳛P{X>i,y>i}=-3.eO5&(x,y)=P{X4x,Y4y},X:yḄὶᔠᑖᦪ.Vx40ᡈy40Y&(x,y)=05x>0,y>0,ijF(x,y)=2££e-2,,e,dwdv-(1-e-2j)(1-ev).,

14(l-e-2r)(l-e-y).x>0,y>0,F(x,y)=0AxWOᡈyWO.&{X>1,Y>1}=jjf(x,y)dxdy=^2ᔆ'*fe'dy=e-3.3.125G,¡¢y=/:£¢y=xᡠ¥ᡂḄ§¨©67ᔣ9(X,Y)ᙠG«ᙳᒴᑖEX:YḄᭆ᳛=>FG(x):/;(y)-O5G,y=x:y=x2ᡠ¥(S)ᐸ☢”?$32301,2,3{(x-x2)dx-=y-y==1006S=S—S—10.5,GQDᐸ)S஺,¡¢y=x2:£¢y=4ᡠ¥ᡂ§¨Ḅ☢S஺,¡¢y=d:£¢y=xᡠ¥ᡂ§¨Ḅ☢.¯QX:°Ḅὶᔠᭆ᳛=>?f(x,y)=\T(xy)eG0,(x,y)WG.(1)XḄ=>xe(-2,0),(x)=£f(x,),)dy=yfdy=y(4-x2)xe(0,2),fஹ(x)=f/(x,>')dy+*f(x,y)dyRfd)+^dy=yU2-x),y(4-x2),-24x<0,ম-x),04x<2..0,ᐸ{.ফyḄ=>o“

15—(2-y),O«y?x+y,OWx,yWL—)=0,ᐸ{.E6789u=x+yḄᭆ᳛=>f(u).O஻<0:஻>2,Zᯠ/Q)=0.(1)50஻(1.½eᑮV஻Y/(X,஻-x)=0.¯Q¿À6789Á:Ḅᭆ᳛=>ÂÃᨵ/(w)=[=£(r+w-t)dt=a2.(2)51K஻42.½eᑮV<஻-1Y/(ᐔ஻-Ç=0.ᵫÀ6789Á:Ḅᭆ᳛=>ÂÃᨵ/(w)=j=f(r+w-t)dt=w(2-u).J-8Jll-1,6789u=x+yḄᭆ᳛=>u~,0/(Z).OVZWOYZᯠ/(z)=oJÔÕÖ×5z>o.(1)54=22=4/(z)=Xe->d஻=.(2)54HÙ.ᵫÀÊË6789Á:ḄᔁÂÃf(z)=44je-*%g)d”=JA_(eÝ_eÞ).

16(B)Dஹᓫ⚗⌱â⚪3.2856789X:°ÈÉÊËᐸᑖᦪÈä?å(x):᜜“)ᑣ67890=1!^<é,°}Ḅᑖᦪ?F(a)=(A)max{F|(஻)K(஻)}.(B)min{l-.(஻),lDì(")}.(C)5(“)&2(“).(D)l-[l-F,()][l-^(«)].[]Mᑖ᪆ä⌱(C).ò,D⍝ôõឋḄᓫ⚗⌱â⚪÷ø£ùôõU=max{X)}ḄᑖᦪᓽRüýþü⌱⚗.ᵫᑖᦪḄýÿ
XḄឋU=max{X,V}ḄᑖᦪF(u)=P{U1,ᐸᑖᦪ

17P[Xy],1”L11y±l.ᵫ"F(x)#ef¤¥¦§¨Ḅᑖᦪy<1¢F(y)<1.(2)᣸◀MᵫV=min{X,l}ḄᑖᦪG(y),·#¸ᦣ-¦§ºᔠ¨»O#¸ᦣ¨¼O#¦§¨}~⌱⚗(A)(C):┯¾.ᑖᦪG(y)¿ᯠ$ᨵW®¯°ᦑ(D)¼#┯¾⌱⚗."#$ᨵ⌱⚗(B)+,.⚪Ḅᩩ´“¤¥¦§¨”XḄ“¤¥”#ÃḄOÄd⌱Å+,⚗ᨵÆ“Ç᡾”Éᵨ.331bx#$ᨵ[WÊËḄ¸ᦣ¨y#¦§¨NÌxyYZᑣX+Ḅᑖᦪ(A)#▤ªᦪ.(B)ា¬ᨵW®¯°.(C)#¦§ᦪ.(D)ា¬ᨵ[W®¯°.[]ÍG⌱(C).Î`▭a#⍝ÑឋḄᓫ⚗⌱Å⚪.Ꮇb(ab}X~p+q-\,IPq)NF(x)#ÔÕ/(x)Ḅ¦§¨ᑖᦪᑣx+yḄᑖᦪG(“)=P{X+Y0>0,ᑣyᐵ"X=xḄᩩ´ÔÕf(xV)—/1,1Iyà\lr2-X2,á(â)=◤=257'101Iy|>3-x2.}~yᐵ"x=iḄᩩ´ᑖ#ᙠà®[-V7=Ai]aḄᙳᒴᑖ.(2)᣸◀MxyḄὶᔠÔÕ—1(x,y)GG,஻x,y)=<7ir01(x,y)eG.XḄÔÕä(x)#ḄåæÔÕ.|x[ு/•¢¿ᯠ/(ᐗ)=0.|xàr¢ᨵ

18E(x)=4᪵ëyḄᭆ᳛ÔÕ1Iyír01Iy|>r.}~X:O;<ᙳᒴᑖ⌱⚗(B)¿ᯠ¼Oᡂ."#⌱⚗(A),(B)ᑭ(C):Oᡂ.ñᙠ⌱⚗(B)Oᡂ._`aA\Ù2=ò-ᭆ᳛ÔÕḄÝÞtg(z)=ô/(z+y,y)dy.Ù2=X-ḄËö¿ᯠ÷-2r,2.}~|z|<2,•¢g(z)=0.ᵫXḄÔÕᙠà®aø"2/ᐔᙠ÷-/•,,ú᜜0,0Wz«r¢ᵫ04z+y4r,04y4r,·04y4r-z,ᦑg(z)=ff(z+y,y)dy=ÿjdy=4(r—z)J"ᐔᔆ,ᐔr;•«z40FhO<^+y⌱⚗(B)B+┯D⌱⚗.*+Eᨵ⌱⚗(D)ᡂI.J⚪LMNOPḄᦪRᱯTJ⚪UV(A)4.3XMNOPXḄᭆ᳛123...\kxa,40cx<1,80,ᐸ].^_EX=0.75,cd_eᦪfgaḄi.Uj⚪X_EX=xf(x)dx==—=-A-=0.75,J—J஺a+2°a+2

19op☢ᵫ*f/(x)dx=fkxadx=—^ߟxa+''k1,J-00a+loa+1*+sᐵ*ugaḄpvwk0.75,஺+2k]ஹa+lᐸU3a=2,k=3.XMNOPXz={ᦪ32Ḅ|}ᑖcE(3X-2).U_{ᦪ32Ḅ|}ᑖḄᦪEX=2,ᦑ£(3X-2)=3£X-2=3x2-2=4.4.6cEX,^_MNOPXᐹᨵᭆ᳛123X,40

20?(?!,)=0.10,P(A)=0.20,P(A)=0.30.ᵫ*ᔜḄ᝱¡Ip{x=o}=P(4AA)=P(A)P(A)P(A)=0.9x0.8x0.7=0.504,p{x=i}=P(A44+A,AA+44A)23=0.1x0.8x0.7+0.9x0.2x0.7+0.9x0.8x0.3=0.398,p{x=2}=P(AAA+AAA+AAA)=0.lx0.2x0.7+0.1x0.8x0.3+0.9x0.2x0.3=0.092,P{X=3}=P(AAA)=P(A)P(4)P(A)=0.1x0.2x0.3=0.006.*+XḄᭆ᳛ᑖ3x40123L(0.5040.2980.0920.006J=>EX=0x0.504+1x0.398+2x0.092+3x0.006=0.6,EX2=()2x0.504+12X0.398+22X0.092+32x0.006=0.820,OX=EX2-(EX)2=0.820-0.62=0.46.4.11XMNOPX1,X”X3¡IX|z=®¯(0,6)°Ḅᙳᒴᑖ>X2±N(0,22),X3²³{ᦪ33Ḅ|}ᑖ´cy=X1-2x?+3X?Ḅp.Uᵫᩩ_஺X1=3,OX2=2,QX3=3,>ᵫpḄឋ¶s£>r=D(X-2X,+3X,)=DX+4DX+9DX1t23=3+4x2+9x3=38.4.12XMNOPXgy¡IX±N(l,2),y±N(0,l),´cMNOP2=2·+3Ḅᦪஹp¸¹ᭆ᳛12.Uᵫᩩ_X±N(l,2),y±N(0,l).=>ᵫpḄឋ¶sEZ=2EX-EY+3=5,DZ=4DX+DY=9.ᵫ*z+xḄºឋᦪx,y+¡IḄ»᝱MNOPᦑzB3»᝱MNOP>»᝱ᑖ¼ᐰ¾*ᐸp¿ÀZ~N(5,9),*+zḄᭆ᳛1231(2-5)2&(z)=^=e2x9(_Vz<+00).003yJ2nஹÁpᐵÂᦪ

214.16^_MNᔣP(X,Y)Ḅᭆ᳛12x+y,40<1,/(x,y)="0,49ᯠ.cEX,EY,DX,DY,EXY,cov(X,K),p.XYU(1)cEX,EROX,OY஺EX=JjÌ•(x,j)dxdy=(xdrj(x+y)dyEX2=jjx2f(x,y)d_xdy=1x2dr£(x+y)dyjÍÎឋᨵ£y4DY=—144(2)cEXÏcov(X,Y),p.XY(•+8f+aoEXY=JJj)/(x,y)drdyJ-ot>J-8=£xdxfy(x+y)dy=#Ð+ÑJa1771cov(X,X)=EXY-EXEY=-----x—=-----31212144cov(X,y)_1/144_1Pxv~4DX4DY~11/144-1114.17XXy+¡I¢ᑖḄÓ¨MNOP^_XḄᭆ᳛ᑖ3P{X=/}=1(/=1,2,3),>MNOPU=max{X,Y},V=min{X,y}.c(1)MNᔣP(U,V)ḄᑖÛ(2)MNOPUḄᦪEU(3)MNOPUgVḄᐵÂᦪP.U(1)ᵫᩩ_Ugᔜᨵ1,2,3Ü3¨ÝiV

22P{U=i,V=j}=P{X=i,Y=j}+P{X=j,Y=i}11112=—x--F—x—=—.33339*+஺gVḄὶᔠᑖgáâᑖ3:§4.17⚪UgVḄὶᔠᑖ¹ᐸáâᑖ123P{U=i}11/9001/922/91/903/932/92/91/95/9P{V=j}5/93/91/91(2)MNOPUḄᦪ13522E(/=lx-+2x-+3x-=—.9999(3)MNOPUgVḄᐵÂᦪ:»I5஺3“114EV=lx—+2x—+3x—=—,9999EU2=l2xl+22x-+32x-=58—A9999£V2=12X-+22X~+32X-!-=26—A9999co38DU=EU2-(EU)2=-^8?38DV=£V2-(£V)2=y8?ìᙠcUgVḄÁp36=lxlx—4-2x1x—+2x2x—4-3x1X-+3X2X—4-3X3X—=——9999999cov(U,V)=EUV-EUEV=---x—=—.99981*+UgḄᐵÂᦪ3cov(t/,V)16/81_8PUV-4DU4DV-38/81-T?(B)ஹᓫ⚗⌱ð⚪4.19XMNOPXz=[1,3]°Ḅᙳᒴᑖᑣ1/XḄ+.(A)(B)2.(C)ô3.(D)ln3.[]

23ᑖ᪆ö⚪÷⌱(C)஺ø+⍝úûឋḄᓫ⚗⌱ð⚪ᦑ¸üýþÿ
ᑮᫀ஺XḄᭆ᳛ᦪ—,14x43,஻x)=<20,ᐸ$.-1ch-=-1lnx21n3.2224.20*X+,-./ᦪ+EX1XḄᦪ+ᑣ(A)E(X—X0)2=E(X—EX)?.(B)E(X-x)2>E(X-EX)2.0(C)E(X-x)2+(EXy-2xEX+xF0=DX+(EX-x)2>DX=E(X-EX)2.0B1(B)⌱⚗.4.21*XyḄKLMᙠ+ᑣ஺(O+O)=஺O+஺O1*O(A)QRᐵḄᐙᑖUVW⌕ᩩZ.(B)QRᐵḄᐙᑖW⌕ᩩZ.(C)[\ḄᐙᑖUQ1W⌕ᩩZ.(D)[\ḄᐙᑖW⌕ᩩZ.1ᑖ᪆=]⌱(B).o(x+y)=ox+£)y1xyQRᐵḄᐙᑖW⌕ᩩZ+=]1`aḄឋc+de]⚪gᵨi⌱j.(1)i⌱jᵫ`aḄlmD(X+Y)=DX+Z)y+2cov(X,y),qr£>«+O)=0O+஺Otuvt(w0O஺,O)=0,xcov(x,y)=oḄᐙᑖW⌕ᩩZ1xOQRᐵ.B1(B)1⌱⚗.(2)᣸◀jᵫBD(X+Y)=DX+DY+2cov(X,y),qrcov(x,y)=o1஺஺+O)=஺*+஺OḄᐙᑖW⌕ᩩZ+de⌱⚗(A)Qᡂ\F`a+D(X+Y)=DX+DY,U1xy|W[\w}᝞+*xyḄὶᔠᑖ1ᙊx2+y2

24ᑖ᪆=⌱(B).§1⍝
ឋḄᓫ⚗⌱⚪஺ᵫ⚪.aEX=//,EY=A-',DX=a2,DY=A-2,E(X+Y)=EX+EY=ju+-RAEX2=£)X+(£'X)2="2+2,crEY2=DY+(EY)2=«°+«2=22,E(X2+Y2)=EX2+EY2=^2+cr2+2A-2.ᡠ¯⌱⚗(A)(C)(D)ᙳ+ᵫBX°V|W[\+x(B)Qᡂ\.4.23*X±IV᝱ᑖ+uQRᐵ+ᑣ(A)X°y³[\.(B)(X,O)´ᐗ᝱ᑖ.(C)X°y|W[\.(D)X+Yᐗ᝱ᑖ.[]ᑖ᪆=⌱(C)஺(1)i⌱j·¸᝱ᑖ+ᯠxᐸὶᔠᑖ|W1᝱ᑖ(r[20]}3.21),de(C)1⌱⚗஺(2)᣸◀j⌱⚗(A)(B)(D)Ḅº⚪┯¼+◤¾¿R=ḄÀ}஺?/@+*XÁN(0Â)஺AB⌱⚗(A),ᵫAឋay=-x~N(o,i),ᯠxxOÃᯠQ[\FAB⌱⚗Ä+(x,y)=(x,-x)ÃᯠQ´ᐗ᝱ᑖFAB⌱⚗(D),X+OÅ஺+X+YQᐗ᝱ᑖ.B1+ᨵ(C)1⌱⚗஺