概率论与数理统计答案.pdf

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1、?1?1.1?1.?2.?3.?1.1?(1)?(2)?(3)?(4)?10?6?4?1 10?(5)?(1)=(1,1),(1,6),(2,1),(2,6),(3,1),(3,6),(4,1),(4,6),(5,1),(5,6),(6,1),(6,6).?(i,j)?i?j?(i,j=1,2,3,4,5,6).(2)=(0,+).(3)=w000,w001,w010,w011,w100,w101,w110,w111,?w000?w110?2?(4)=1,2,3,4,5,6,7,8,9,10.(5)?=(x,y)|x2+y2 1,?=(,),1,0?2.?1.2?A,B,C?A,B,C?(1)

2、A?B?C?(2)A?B?C?(3)A,B,C?(4)A,B,C?(5)A,B,C?(6)A,B,C?(7)A,B,C?(8)A,B,C?Di(i=1,2,3,8)?(1),(2),(8)?A?A?(1)D1=AB C?D1=A B C.(2)D2=ABC?D2=AB C.(3)D3=A B C?D3=A B C,?D3=AB C ABC A BC ABC ABC ABC ABC.(4)D4=ABC.(5)D5=A B C.(6)D6=A B C AB C ABC A BC?D6=AB BC CA=AB BC CA.(7)D7=A B C AB C ABC A BC ABC ABC ABC?D

3、7=A B C?D7=ABC.(8)D8=AB BC CA?D8=ABC ABC ABC ABC.?1.3?Ai?i?(i=1,2,3),?A1 A2;A2;A1 A2A3;A1A2A3;A3 A2;A1 A2;A1A2;A2 A3;A2A3;A1A2 A1A3 A2A3.?A1 A2?A2?A1 A2 A3?A1A2A3?A3 A2?1?3A1 A2=A1A2?A2 A3=A2A3?A1A2 A1A3 A2A3?1.4?(1)AB=A B;(2)?AB=,?C A,?BC=;(3)AB AB=;(4)?A B,?A B;(5)A B=A B;(6)(A B)C=A B C.?(1)?A?A.

4、(2)?BC?=,?C A,?BA?=,?(3)?B,B?AB?AB?(4)?B?A?A?A B,?B?B B,?(5)?A B=?AB?=A B,?A B=A B.(6)?(A B)C=A B C.?1.5?A B,P(A)=0.2,P(B)=0.3,?(1)P?A?;(2)P?B?;(3)P(AB);(4)P(A B);(5)P?BA?;(6)P(A B).?(1)P?A?=1 P(A)=1 0.2=0.8;(2)P?B?=1 P(B)=1 0.3=0.7.(3)P(AB)=P(A)=0.2.(4)P(A B)=P(A)+P(B)P(AB)=0.3.(5)P?BA?=P(B(A)=P(B)

5、P(AB)=P(B)P(A)=0.3 0.2=0.1.(6)P(A B)=0.?1.6?P(A)=0.4,P(B)=0.25,P(A B)=0.25,?P(AB),P(A B),P(B A),P?A B?.?P(AB)=P(A)P(A B)=0.4 0.25=0.15;P(A B)=P(A)+P(B)P(AB)=0.4+0.25 0.15=0.5;P(B A)=P(B)P(AB)=0.25 0.15=0.1;P?A B?=P?A B?=1 P(A B)=1 0.5=0.5.4?1.7?A,B?P(A B)P(AB)?P(A)P(B).?P(A B)P(AB)=P(A B)P(AB)+P(B A

6、)P(AB)+P(AB)P(AB)?P(A B)P(B A)+P(A B)P(AB)+P(B A)P(AB)+P(AB)P(AB)=P(A B)+P(AB)P(B A)+P(AB)=P(A)P(B).?P(A B)P(AB)?P(A)P(B).?1.8?A?B?C?().(A)P(C)=P(AB);(B)P(C)?P(A)+P(B)1;(C)P(C)=P(A B);(D)P(C)?P(A)+P(B)1.?P(C)?P(AB),?P(AB)=P(A)+P(B)P(A B)?P(A)+P(B)1.?(B).?1.9?2?3?5?5?10?5?C510,?A(?5?)?(1)?2?5?3?C22C3

7、3+C22C23C15+C22C13C25+C22C35;(2)?1?5?2?2?C12C33C15+C12C23C25.?A?C22C33+C22C23C15+C22C13C25+C22C35+C12C23C15+C12C23C25=126.?1?5?P(A)=126C510=12.?1.10?10?3?(1)?3?2?(2)?3?2?(1)?A?3?2?10?3?n=C310?A,?3?2?C23?1?C17?A?C23C17?P(A)=C23C17C310=21120=740.(2)?B?3?2?10?103?B,3?2?C23?3 3=32?7?B?C23 32 7?P(B)=C23

8、32 7103=0.189.?1.11?r?r?365.?365?r?r?365?365r,?A?r?A?365?r?Pr365=365!(365 r)!.?P(A)=365!(365 r)!365r.?1.12?1,2,3,4,5?5?1,2,10?10?5?10?5?(1)?5?(2)?1?(3)?6?5?10?10?105?(1)?A?5?1?A?5?nA=5!,?P(A)=5!105=0.0012.(2)?B?B?5?10?5?C510?5?5!?nB=C510 5!,?P(B)=C510 5!105=0.3024.(3)?C?C?C?5?9?95?P(C)=1 P(C)=1 9510

9、5=0.40951.?1.13?(52?)?3?(?),?3?2?A?3?2?A,?3?4?3?1?A?C34C113C113C113.?C352,?P(A)=1 P(A)=1 C34C113C113C113C352 0.602.?1.14?5?4?4?A?4?A?4?15?4?C410=210?A?4?5?4?4?C4524=80?P(A)=1 P(A)=1 80210=1321.?1?7?25?4?C410=210?4?5?1?4?2?C15C28?C25.?nA=C15C28C25,?P(A)=C15C28 C25C410=1321.?3?A1?4?A2?4?A=A1 A2,?P(A1)

10、=C15?C28 C14?C410,P(A2)=C25C410.?P(A)=P(A1)+P(A2)=C19?C28 C14?C410+C25C410=1321.?1.15?1,2,3,9?9?n?n?10?9?n?9n.?A?n?10?A?n?10?10=2 5,?A?B?n?5?C?n?5,?2,4,6,8?B?C?A=B C.B?1,2,3,4,6,7,8,9,?8?n?8n?P(B)=8n9n.C?1,3,5,7,9,?5?n?5n?1,3,7,9?4?n?4n?5n 4n?P(C)=5n 4n9n,?P(A)=1 P(A)=1 P(B C)=1 8n+5n 4n9n.?1.16?n?n

11、?r(r n 1)?n?r?r?(?).8?n?n!?A=?r?,?1?C12?(?)?i?(?)?i+n1?i+r+1?n,?i?n r 1.?n r 1?n 2?(n 2)!?P(A)=C12(n r 1)(n 2)!n!=2(n r 1)n(n 1).?n?(n 1)!?n?r?(n r 1)(n 2)!?n?r?n r 2?X?nr 1?(n r 1)(n 2)!=X(n r 1),?X=(n 2)!.?A?(n 2)!?P(A)=(n 2)!(n 1)!=1n 1?r?1.17?3?1?1?G(?1.1);?P=G?=9 19=89.33G331111?1.1OA(,)20axy(,

12、)a04?1.2?1?9?1.18?0 y 2ax x2(a?)?x?4?(x a)2+y2=a2?(?1.2),?a22.?A=?x?4,?A?=?40d?2a cos0rdr=a22+a24,?P(A)=a22+a242a2=12+1.?1.?AB=,?A?B?A,?A?A?A.A?A?1?5?4?4?2.?10?1?=(?),(?),(?),(?),A=(?),(?),P(A)=24=12.?2?=(?),(?),A=?,P(A)=12.?3?=(i,j)|i,j=1,2,6,?6 6=36;?A?2 3 3=18,P(A)=1836=12.?3.?(1)?(2)?(2)?(1).?=(?),(?),(?),(?),A=(?),(?),?P(A)=24=12.?=(?),(?),(?)A=(?),(?),?P(A)=23.?P(?)=14,P(?)=12.?1.11.?(1)?10?6?1 10?(2)?(3)?(4)?1?