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高等数学概率论与数理统计《初等概率论》PPT课件-第1讲.pdf

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1、5?V6118?V?.81?2V?.15?V6118?V?.!?81.Vg18?3/8.i1S?L2?8p?.?i1LXx,y,a,b,c?.38?8P.2.8?L1?S=x1,x2,.,xn,.,XJSk?XS=H,T S=1,2,.,6S=1,2,.2xk,5P5x8Px|xv5P,Xx|0 x 1.25?V6118?V?.!?81.Vg18?3/8.i1S?L2?8p?.?i1LXx,y,a,b,c?.38?8P.2.8?L1?S=x1,x2,.,xn,.,XJSk?XS=H,T S=1,2,.,6S=1,2,.2xk,5P5x8Px|xv5P,Xx|0 x 1.35?V6118?V?.

2、!?81.Vg18?3/8.i1S?L2?8p?.?i1LXx,y,a,b,c?.38?8P.2.8?L1?S=x1,x2,.,xn,.,XJSk?XS=H,T S=1,2,.,6S=1,2,.2xk,5P5x8Px|xv5P,Xx|0 x 1.45?V6118?V?.!?81.Vg18?3/8.i1S?L2?8p?.?i1LXx,y,a,b,c?.38?8P.2.8?L1?S=x1,x2,.,xn,.,XJSk?XS=H,T S=1,2,.,6S=1,2,.2xk,5P5x8Px|xv5P,Xx|0 x 1.55?V6118?V?.!?81.Vg18?3/8.i1S?L2?8p?.?i1LX

3、x,y,a,b,c?.38?8P.2.8?L1?S=x1,x2,.,xn,.,XJSk?XS=H,T S=1,2,.,6S=1,2,.2xk,5P5x8Px|xv5P,Xx|0 x 1.65?V6118?V?.!?81.Vg18?3/8.i1S?L2?8p?.?i1LXx,y,a,b,c?.38?8P.2.8?L1?S=x1,x2,.,xn,.,XJSk?XS=H,T S=1,2,.,6S=1,2,.2xk,5P5x8Px|xv5P,Xx|0 x 1.75?V6118?V?.!?81.Vg18?3/8.i1S?L2?8p?.?i1LXx,y,a,b,c?.38?8P.2.8?L1?S=x1,x

4、2,.,xn,.,XJSk?XS=H,T S=1,2,.,6S=1,2,.2xk,5P5x8Px|xv5P,Xx|0 x 1.85?V6118?V?.?83.X1?8?X?x8S?Xox S,ox/S.288?Xf8e8S?k?8T?ST?f8PS TT S.AO/S.?eS TT SKS=T.3?a,?k?3/8d8mP.?(?8S?f8.95?V6118?V?.?83.X1?8?X?x8S?Xox S,ox/S.288?Xf8e8S?k?8T?ST?f8PS TT S.AO/S.?eS TT SKS=T.3?a,?k?3/8d8mP.?(?8S?f8.105?V6118?V?.?83.X1

5、?8?X?x8S?Xox S,ox/S.288?Xf8e8S?k?8T?ST?f8PS TT S.AO/S.?eS TT SKS=T.3?a,?k?3/8d8mP.?(?8S?f8.115?V6118?V?.?83.X1?8?X?x8S?Xox S,ox/S.288?Xf8e8S?k?8T?ST?f8PS TT S.AO/S.?eS TT SKS=T.3?a,?k?3/8d8mP.?(?8S?f8.125?V6118?V?.?83.X1?8?X?x8S?Xox S,ox/S.288?Xf8e8S?k?8T?ST?f8PS TT S.AO/S.?eS TT SKS=T.3?a,?k?3/8d8m

6、P.?(?8S?f8.135?V6118?V?.?83.X1?8?X?x8S?Xox S,ox/S.288?Xf8e8S?k?8T?ST?f8PS TT S.AO/S.?eS TT SKS=T.3?a,?k?3/8d8mP.?(?8S?f8.145?V6118?V?.?84.$18(Complement)8x|x/S8S?8PSc.AO/c=.28(Union)duSuT?|?8ST?PS T.3?8(Intersection)duSuT?|?8ST?PS T.4?8(difference)duS?uT?|?8ST?8PS T.w,S T=S Tc.5?8(symmetric differen

7、ce)PS 4 T.w,S 4T=(S Tc)(T Sc).155?V6118?V?.?84.$18(Complement)8x|x/S8S?8PSc.AO/c=.28(Union)duSuT?|?8ST?PS T.3?8(Intersection)duSuT?|?8ST?PS T.4?8(difference)duS?uT?|?8ST?8PS T.w,S T=S Tc.5?8(symmetric difference)PS 4 T.w,S 4T=(S Tc)(T Sc).165?V6118?V?.?84.$18(Complement)8x|x/S8S?8PSc.AO/c=.28(Union)

9、S Tc.5?8(symmetric difference)PS 4 T.w,S 4T=(S Tc)(T Sc).185?V6118?V?.?84.$18(Complement)8x|x/S8S?8PSc.AO/c=.28(Union)duSuT?|?8ST?PS T.3?8(Intersection)duSuT?|?8ST?PS T.4?8(difference)duS?uT?|?8ST?8PS T.w,S T=S Tc.5?8(symmetric difference)PS 4 T.w,S 4T=(S Tc)(T Sc).195?V6118?V?.?84.$18(Complement)8x

13、?S?c=Sc.285?V6118?V?.?86.8?“8$?eZ51S T=T S;(?)2S (T U)=(S T)U;()3S (T U)=(S T)(S U),S (T U)=(S T)(S U),(?)4(Sc)c=S,S Sc=,5S =,S =S.:De:Morgans:laws(?K)?S?c=Sc,?S?c=Sc.295?V6118?V?.?86.8?“8$?eZ51S T=T S;(?)2S (T U)=(S T)U;()3S (T U)=(S T)(S U),S (T U)=(S T)(S U),(?)4(Sc)c=S,S Sc=,5S =,S =S.:De:Morgan

14、s:laws(?K)?S?c=Sc,?S?c=Sc.305?V6118?V?.?86.8?“8$?eZ51S T=T S;(?)2S (T U)=(S T)U;()3S (T U)=(S T)(S U),S (T U)=(S T)(S U),(?)4(Sc)c=S,S Sc=,5S =,S =S.:De:Morgans:laws(?K)?S?c=Sc,?S?c=Sc.315?V6118?V?.?86.8?“8$?eZ51S T=T S;(?)2S (T U)=(S T)U;()3S (T U)=(S T)(S U),S (T U)=(S T)(S U),(?)4(Sc)c=S,S Sc=,5S

15、 =,S =S.:De:Morgans:laws(?K)?S?c=Sc,?S?c=Sc.325?V6118?V?.?86.8?“8$?eZ51S T=T S;(?)2S (T U)=(S T)U;()3S (T U)=(S T)(S U),S (T U)=(S T)(S U),(?)4(Sc)c=S,S Sc=,5S =,S =S.:De:Morgans:laws(?K)?S?c=Sc,?S?c=Sc.335?V6118?V?.?86.8?“8$?eZ51S T=T S;(?)2S (T U)=(S T)U;()3S (T U)=(S T)(S U),S (T U)=(S T)(S U),(?

16、)4(Sc)c=S,S Sc=,5S =,S =S.:De:Morgans:laws(?K)?S?c=Sc,?S?c=Sc.345?V6118?V?.?86.8?“8$?eZ51S T=T S;(?)2S (T U)=(S T)U;()3S (T U)=(S T)(S U),S (T U)=(S T)(S U),(?)4(Sc)c=S,S Sc=,5S =,S =S.:De:Morgans:laws(?K)?S?c=Sc,?S?c=Sc.355?V6118?V?.?86.8?“8$?eZ51S T=T S;(?)2S (T U)=(S T)U;()3S (T U)=(S T)(S U),S (

17、T U)=(S T)(S U),(?)4(Sc)c=S,S Sc=,5S =,S =S.:De:Morgans:laws(?K)?S?c=Sc,?S?c=Sc.365?V6118?V?.?86.8?“8$?eZ51S T=T S;(?)2S (T U)=(S T)U;()3S (T U)=(S T)(S U),S (T U)=(S T)(S U),(?)4(Sc)c=S,S Sc=,5S =,S =S.:De:Morgans:laws(?K)?S?c=Sc,?S?c=Sc.375?V6118?V?.?!V?.V?.?m:?:k:U:(:J?8V(probability)V?(J?8A()(KP

18、(A)(A?V).dKx?A?)?&g.:V?.?385?V6118?V?.?!V?.V?.?m:?:k:U:(:J?8V(probability)V?(J?8A()(KP(A)(A?V).dKx?A?)?&g.:V?.?395?V6118?V?.?!V?.V?.?m:?:k:U:(:J?8V(probability)V?(J?8A()(KP(A)(A?V).dKx?A?)?&g.:V?.?405?V6118?V?.V?.1.?m1zV?.X?)?(J.T?:k:U:(:J/?mP.2?m?(J:U:k:U:?(J|.3?do?vko,?V?.?K?9?Y?ngM1?Ug?Ung?.4?m?f

19、8=,?(J?8:.415?V6118?V?.V?.1.?m1zV?.X?)?(J.T?:k:U:(:J/?mP.2?m?(J:U:k:U:?(J|.3?do?vko,?V?.?K?9?Y?ngM1?Ug?Ung?.4?m?f8=,?(J?8:.425?V6118?V?.V?.1.?m1zV?.X?)?(J.T?:k:U:(:J/?mP.2?m?(J:U:k:U:?(J|.3?do?vko,?V?.?K?9?Y?ngM1?Ug?Ung?.4?m?f8=,?(J?8:.435?V6118?V?.V?.1.?m1zV?.X?)?(J.T?:k:U:(:J/?mP.2?m?(J:U:k:U:?(J|

20、.3?do?vko,?V?.?K?9?Y?ngM1?Ug?Ung?.4?m?f8=,?(J?8:.445?V6118?V?.V?.1.?m1zV?.X?)?(J.T?:k:U:(:J/?mP.2?m?(J:U:k:U:?(J|.3?do?vko,?V?.?K?9?Y?ngM1?Ug?Ung?.4?m?f8=,?(J?8:.455?V6118?V?.V?.2.J?m13(?(J7L:p:?3?LU?)?(J.2?,?(?.?(?.U?m?(J.f1?iZ?9Y?10gM1.1zg?M1?y?I1?a(10g?gk)2?y1g?()g)I1?aUY?1?gy?I2?azg?zg?M1I?aczg?

21、M1I?a?.(=gky?Sk)465?V6118?V?.V?.2.J?m13(?(J7L:p:?3?LU?)?(J.2?,?(?.?(?.U?m?(J.f1?iZ?9Y?10gM1.1zg?M1?y?I1?a(10g?gk)2?y1g?()g)I1?aUY?1?gy?I2?azg?zg?M1I?aczg?M1I?a?.(=gky?Sk)475?V6118?V?.V?.2.J?m13(?(J7L:p:?3?LU?)?(J.2?,?(?.?(?.U?m?(J.f1?iZ?9Y?10gM1.1zg?M1?y?I1?a(10g?gk)2?y1g?()g)I1?aUY?1?gy?I2?azg?zg?M

22、1I?aczg?M1I?a?.(=gky?Sk)485?V6118?V?.V?.2.J?m13(?(J7L:p:?3?LU?)?(J.2?,?(?.?(?.U?m?(J.f1?iZ?9Y?10gM1.1zg?M1?y?I1?a(10g?gk)2?y1g?()g)I1?aUY?1?gy?I2?azg?zg?M1I?aczg?M1I?a?.(=gky?Sk)495?V6118?V?.V?.2.J?m13(?(J7L:p:?3?LU?)?(J.2?,?(?.?(?.U?m?(J.f1?iZ?9Y?10gM1.1zg?M1?y?I1?a(10g?gk)2?y1g?()g)I1?aUY?1?gy?I2?

23、azg?zg?M1I?aczg?M1I?a?.(=gky?Sk)505?V6118?V?.V?.2.J?m13(?(J7L:p:?3?LU?)?(J.2?,?(?.?(?.U?m?(J.f1?iZ?9Y?10gM1.1zg?M1?y?I1?a(10g?gk)2?y1g?()g)I1?aUY?1?gy?I2?azg?zg?M1I?aczg?M1I?a?.(=gky?Sk)515?V6118?V?.V?.2.J?m13(?(J7L:p:?3?LU?)?(J.2?,?(?.?(?.U?m?(J.f1?iZ?9Y?10gM1.1zg?M1?y?I1?a(10g?gk)2?y1g?()g)I1?aUY?

24、1?gy?I2?azg?zg?M1I?aczg?M1I?a?.(=gky?Sk)525?V6118?V?.V?.3.S0?.?kS0?A?XY?qM1?ngY*?*U:S:0:/:5x?m?(J:S0/535?V6118?V?.V?.3.S0?.?kS0?A?XY?qM1?ngY*?*U:S:0:/:5x?m?(J:S0/545?V6118?V?.V?.3.S0?.?kS0?A?XY?qM1?ngY*?*U:S:0:/:5x?m?(J:S0/555?V6118?V?.V?.4.VVn1(K5)AvP(A)0.2(?5)eA1,A2,.pN?S?vP?n=1An?=Xn=1P(An).3(8z)

25、P()=1.V?eZ51eA B,KP(A)P(B).2P(A B)=P(A)+P(B)P(A B).3P(A B)P(A)+P(B).4P(A B C)=P(A)+P(Ac B)+P(Ac Bc C).565?V6118?V?.V?.4.VVn1(K5)AvP(A)0.2(?5)eA1,A2,.pN?S?vP?n=1An?=Xn=1P(An).3(8z)P()=1.V?eZ51eA B,KP(A)P(B).2P(A B)=P(A)+P(B)P(A B).3P(A B)P(A)+P(B).4P(A B C)=P(A)+P(Ac B)+P(Ac Bc C).575?V6118?V?.V?.4.V

26、Vn1(K5)AvP(A)0.2(?5)eA1,A2,.pN?S?vP?n=1An?=Xn=1P(An).3(8z)P()=1.V?eZ51eA B,KP(A)P(B).2P(A B)=P(A)+P(B)P(A B).3P(A B)P(A)+P(B).4P(A B C)=P(A)+P(Ac B)+P(Ac Bc C).585?V6118?V?.V?.4.VVn1(K5)AvP(A)0.2(?5)eA1,A2,.pN?S?vP?n=1An?=Xn=1P(An).3(8z)P()=1.V?eZ51eA B,KP(A)P(B).2P(A B)=P(A)+P(B)P(A B).3P(A B)P(A)+

27、P(B).4P(A B C)=P(A)+P(Ac B)+P(Ac Bc C).595?V6118?V?.V?.4.VVn1(K5)AvP(A)0.2(?5)eA1,A2,.pN?S?vP?n=1An?=Xn=1P(An).3(8z)P()=1.V?eZ51eA B,KP(A)P(B).2P(A B)=P(A)+P(B)P(A B).3P(A B)P(A)+P(B).4P(A B C)=P(A)+P(Ac B)+P(Ac Bc C).605?V6118?V?.V?.4.VVn1(K5)AvP(A)0.2(?5)eA1,A2,.pN?S?vP?n=1An?=Xn=1P(An).3(8z)P()=1

28、.V?eZ51eA B,KP(A)P(B).2P(A B)=P(A)+P(B)P(A B).3P(A B)P(A)+P(B).4P(A B C)=P(A)+P(Ac B)+P(Ac Bc C).615?V6118?V?.V?.4.VVn1(K5)AvP(A)0.2(?5)eA1,A2,.pN?S?vP?n=1An?=Xn=1P(An).3(8z)P()=1.V?eZ51eA B,KP(A)P(B).2P(A B)=P(A)+P(B)P(A B).3P(A B)P(A)+P(B).4P(A B C)=P(A)+P(Ac B)+P(Ac Bc C).625?V6118?V?.V?.4.VVn1(K

29、5)AvP(A)0.2(?5)eA1,A2,.pN?S?vP?n=1An?=Xn=1P(An).3(8z)P()=1.V?eZ51eA B,KP(A)P(B).2P(A B)=P(A)+P(B)P(A B).3P(A B)P(A)+P(B).4P(A B C)=P(A)+P(Ac B)+P(Ac Bc C).635?V6118?V?.V?.4.VVn1(K5)AvP(A)0.2(?5)eA1,A2,.pN?S?vP?n=1An?=Xn=1P(An).3(8z)P()=1.V?eZ51eA B,KP(A)P(B).2P(A B)=P(A)+P(B)P(A B).3P(A B)P(A)+P(B).

30、4P(A B C)=P(A)+P(Ac B)+P(Ac Bc C).645?V6118?V?.V?.:|?*?yV?5655?V6118?V?.V?.5.l?.f2?qM1?k(J:?HT.?m=H,T.H,T,H,T,.eM1!?=&3?M1?k?y=P(H)=P(T)=1/2.dP(H,T)=1,P(H)=P(T)=1/2,P()=0.665?V6118?V?.V?.5.l?.f2?qM1?k(J:?HT.?m=H,T.H,T,H,T,.eM1!?=&3?M1?k?y=P(H)=P(T)=1/2.dP(H,T)=1,P(H)=P(T)=1/2,P()=0.675?V6118?V?.V?.5

31、.l?.f2?qM1?k(J:?HT.?m=H,T.H,T,H,T,.eM1!?=&3?M1?k?y=P(H)=P(T)=1/2.dP(H,T)=1,P(H)=P(T)=1/2,P()=0.685?V6118?V?.V?.5.l?.f2?qM1?k(J:?HT.?m=H,T.H,T,H,T,.eM1!?=&3?M1?k?y=P(H)=P(T)=1/2.dP(H,T)=1,P(H)=P(T)=1/2,P()=0.695?V6118?V?.V?.5.l?.f2?qM1?k(J:?HT.?m=H,T.H,T,H,T,.eM1!?=&3?M1?k?y=P(H)=P(T)=1/2.dP(H,T)=1,P

32、(H)=P(T)=1/2,P()=0.705?V6118?V?.V?.5.l?.f2?qM1?k(J:?HT.?m=H,T.H,T,H,T,.eM1!?=&3?M1?k?y=P(H)=P(T)=1/2.dP(H,T)=1,P(H)=P(T)=1/2,P()=0.715?V6118?V?.V?.5.l?.f2?qM1?k(J:?HT.?m=H,T.H,T,H,T,.eM1!?=&3?M1?k?y=P(H)=P(T)=1/2.dP(H,T)=1,P(H)=P(T)=1/2,P()=0.725?V6118?V?.V?.f3g?3qM1?(Jd?|?3?S?.?m=HHH,HHT,HTH,HTT,TH

33、H,THT,TTH,TTT.b8(J?U5?=z(J?V1/8.OA=?V.A=HHT,HTH,THH,dP(A)=P(HHT,HTH,THH)=P(HHT)+P(HTH)+P(THH)=1/8+1/8+1/8=3/8.735?V6118?V?.V?.f3g?3qM1?(Jd?|?3?S?.?m=HHH,HHT,HTH,HTT,THH,THT,TTH,TTT.b8(J?U5?=z(J?V1/8.OA=?V.A=HHT,HTH,THH,dP(A)=P(HHT,HTH,THH)=P(HHT)+P(HTH)+P(THH)=1/8+1/8+1/8=3/8.745?V6118?V?.V?.f3g?3qM

34、1?(Jd?|?3?S?.?m=HHH,HHT,HTH,HTT,THH,THT,TTH,TTT.b8(J?U5?=z(J?V1/8.OA=?V.A=HHT,HTH,THH,dP(A)=P(HHT,HTH,THH)=P(HHT)+P(HTH)+P(THH)=1/8+1/8+1/8=3/8.755?V6118?V?.V?.f3g?3qM1?(Jd?|?3?S?.?m=HHH,HHT,HTH,HTT,THH,THT,TTH,TTT.b8(J?U5?=z(J?V1/8.OA=?V.A=HHT,HTH,THH,dP(A)=P(HHT,HTH,THH)=P(HHT)+P(HTH)+P(THH)=1/8+1

35、/8+1/8=3/8.765?V6118?V?.V?.f3g?3qM1?(Jd?|?3?S?.?m=HHH,HHT,HTH,HTT,THH,THT,TTH,TTT.b8(J?U5?=z(J?V1/8.OA=?V.A=HHT,HTH,THH,dP(A)=P(HHT,HTH,THH)=P(HHT)+P(HTH)+P(THH)=1/8+1/8+1/8=3/8.775?V6118?V?.V?.f3g?3qM1?(Jd?|?3?S?.?m=HHH,HHT,HTH,HTT,THH,THT,TTH,TTT.b8(J?U5?=z(J?V1/8.OA=?V.A=HHT,HTH,THH,dP(A)=P(HHT,H

36、TH,THH)=P(HHT)+P(HTH)+P(THH)=1/8+1/8+1/8=3/8.785?V6118?V?.V?.lV?mdkU?(J|K?Vd|?(J?Vs1,s2,.,sn?VP(si)=P(s1,s2,.,sm)=mXi=1P(si).e=s1,.,snz?(J?V?Kl!V(?;V.)?mdn:?:U:5?(J|dz?(J|?(?)?V?.dd?P(A)=uA?(Jn.795?V6118?V?.V?.lV?mdkU?(J|K?Vd|?(J?Vs1,s2,.,sn?VP(si)=P(s1,s2,.,sm)=mXi=1P(si).e=s1,.,snz?(J?V?Kl!V(?;V.)

37、?mdn:?:U:5?(J|dz?(J|?(?)?V?.dd?P(A)=uA?(Jn.805?V6118?V?.V?.lV?mdkU?(J|K?Vd|?(J?Vs1,s2,.,sn?VP(si)=P(s1,s2,.,sm)=mXi=1P(si).e=s1,.,snz?(J?V?Kl!V(?;V.)?mdn:?:U:5?(J|dz?(J|?(?)?V?.dd?P(A)=uA?(Jn.815?V6118?V?.V?.6.Y?.f4?3,?z?/:?mkm30 1?.1?/:?3?15?15?evkyk?lm?/:.U?Vk?IX?/=0,1 0,1.?/?z:?IOLU?m.?f8y?Vf8?.d

38、V?nn.-M=(x,y)|x y|1/4,0 x 1,0 y 1.K?V=M?.V7/16.825?V6118?V?.V?.6.Y?.f4?3,?z?/:?mkm30 1?.1?/:?3?15?15?evkyk?lm?/:.U?Vk?IX?/=0,1 0,1.?/?z:?IOLU?m.?f8y?Vf8?.dV?nn.-M=(x,y)|x y|1/4,0 x 1,0 y 1.K?V=M?.V7/16.835?V6118?V?.V?.6.Y?.f4?3,?z?/:?mkm30 1?.1?/:?3?15?15?evkyk?lm?/:.U?Vk?IX?/=0,1 0,1.?/?z:?IOLU?m.?

39、f8y?Vf8?.dV?nn.-M=(x,y)|x y|1/4,0 x 1,0 y 1.K?V=M?.V7/16.845?V6118?V?.V?.6.Y?.f4?3,?z?/:?mkm30 1?.1?/:?n?/?3.L?mAL?uu?u3.875?V6118?V?.V?.7.?.yf5(BertrandK)31?S?uuu?u3?V.?S?n?/?3.L?mAL?uu?u3.885?V6118?V?.V?.7.?.yf5(BertrandK)31?S?uuu?u3?V.?S?n?/?3.L?mAL?uu?u3.895?V6118?V?.V?.7.?.yf5(BertrandK)31?S?uu

40、u?u3?V.?S?n?/?3.L?mAL?uu?u3.905?V6118?V?.V?.7.?.yf5(BertrandK)31?S?uuu?u3?V.?S?n?/?3.L?mAL?uu?u3.915?V6118?V?.V?.7.?.yf5(BertrandK)31?S?uuu?u3?V.?S?n?/?3.L?mAL?uu?u3.925?V6118?V?.V?.(1).XJu?:?U?3?K:x0(?,:y?U?3?(a).=y|y 0,2),A=y|2/3 y 4/3.uP(A)=1/3.(2).XJu?:?U?3?S(b)K?A?.dP=1/4.(3).XJu?:?U?3R?(c)?=?:

41、?%?l?u1/2?uu3.dP(A)=1/2.l?w?Ub?O(J.935?V6118?V?.V?.(1).XJu?:?U?3?K:x0(?,:y?U?3?(a).=y|y 0,2),A=y|2/3 y 4/3.uP(A)=1/3.(2).XJu?:?U?3?S(b)K?A?.dP=1/4.(3).XJu?:?U?3R?(c)?=?:?%?l?u1/2?uu3.dP(A)=1/2.l?w?Ub?O(J.945?V6118?V?.V?.(1).XJu?:?U?3?K:x0(?,:y?U?3?(a).=y|y 0,2),A=y|2/3 y 4/3.uP(A)=1/3.(2).XJu?:?U?3?S(b)K?A?.dP=1/4.(3).XJu?:?U?3R?(c)?=?:?%?l?u1/2?uu3.dP(A)=1/2.l?w?Ub?O(J.955?V6118?V?.V?.(1).XJu?:?U?3?K:x0(?,:y?U?3?(a).=y|y 0,2),A=y|2/3 y 4/3.uP(A)=1/3.(2).XJu?:?U?3?S(b)K?A?.dP=1/4.(3).XJu?:?U?3R?(c)?=?:?%?l?u1/2?uu3.dP(A)=1/2.l?w?Ub?O(J.96

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