概率论与数理统计浙大第四版答案第二章.pdf

q d95= Is a|B R0 Q 9 V U Q 9 V U Q Kl ksY p9 9 s pb 9 V | aaaaaaaaaa 36 1 6 1 6 1 )1,1()2( 1 = PXP 36 2 6 1 6 1 6 1 6 1 )1,22,1()3( 1 =+= PXP 36 3 6 1 6 1 6 1 6 1 6 1 6 1 )1,32,23,1()4( 1 =+= PXP ll 9 s p 9 1 L 9 V | aaaaa 1 9 1 1,61,51,41,31,26,15,14,13,12,11,1 36 11 9 s p 9 1 L a Q V | X V U |Q pX s pb X V | aa 3 10 3 8 0 C C XP = 15 7 = 15 7 1 3 10 2 8 1 2 = C CC XP 15 1 2 3 10 1 8 2 2 = C CC XP a kb ! Q k q )10( = k k ckXP k k c 1 11 = = a N a kXP N k N k 1=a 12 3 2 1 3 2 3 2 11 = = = = = b b bkXP k k k 2 1 =b 1 ! 00 = = = ec k ckXP k k k = ec a ! M X s p 5,4,3,2,1, 15 = k k kXP sf k p)(xF 2 5 2 1 XP 21 XP 5 1 F 21 2 5 2 1 =+= XPXPXP 5 1 15 2 15 1 =+= 21 XP 21 =+= XPXP 5 1 15 2 15 1 =+= 5 1 F 0 5 1 = = XP aBv L !b V B H Y t !$ P q pB H Y1.0 !$ P q !$ P q !$ P qb ! X V U !$ P 5 )1.0,5( bX ()()0729.09.01.02 32 2 5 = CXP 4095.09.01011 5 = XPxp = 5413 XPXPxp ( ) ( ) ( ) 99954.01.09.01.01 5 5 5 14 4 5 = CC aJa Y Mb VG L ?|J G k G k q $ YV us k Q T Q N us ? $ !Q LM p q 70 11 4 8 = C 7 k QQ X 5 ) 70 1 ,10( bX 4733 10 1016.3) 70 69 () 70 1 (3 = CXP A 3=X Bl q Y l q Yq L= V ? 3 V N B us ? a g r V sb H1 N ? N g q ! 9V Ug r 51 P 999.0 ! 3 0 3 = = x k k k e V 001.0999.01000292.0 ! 3 11 3 = 10 1 10 10 )92.0()08.0( nk kkk CnXP )8.0( ! 1 = + += nk k k e V 2,31 =+ nn H 05.00474.02 XP H 1=n 05.0551.01 =XP 1 ! aBN _ ?v YVb ! B? HW = Y# q b ? HW = Y#Q l q $ ! Y#Q 9 p 3XP 3.00001.03000 = np 3XP 0036.0 ! 3.0 3 3.0 = + = k k k e Y#Q l q ! 9V=s s p ( ) knkk n ppCkXP = 1 ,llO , | H kXP = Kv$ ! 9V s s q !k e kXp k = Lll , | H Kv$kXP = = = = = 1kXP kXP M ( ) () 111 1 1 + knkk n knkk n PPC pPC ( ) = + = kq Pkn 1 ( ) kq kqPknkq + 1 ()( ) kq kqpPn + += 1 1 1,)1( + Mpnk H 1,)1( =+= Mpnk H N H 1= kXPkXP 1,)1( Mpnk H ( ) + + = d pnpn pnpnpn k 11 )1(,)1(,11 s )(P kkP kP = );1( );( l .3,2=k V =k H PP =),( );1( # V sY );( kP M k H 6i O =k H rKv );( P Vk ?M H );( kP / = d , ,1, k a s=ssf a ! M 9sf p = 11 10 00 )( 2 x xAx x xF A q f 2/1XP b20 XP EB M 9sf AAxxFF xx = 2 11 lim)(lim11 = 10 102 00 )()( x xx x XFxf 4/12)(2/1 2/1 0 2/1 = FXPXP =+= 1 0 2 1 2 0 102)(20 dxxdxdxxfXP 101)0()2(20 = FFXP E= = 10 102 00 )()( x xAx x XFxf 12)(1 1 0 = + AAAxdxdxxf EB aX M 9 q = 0 212 10 )( xx xx xf p sf )(XF 2.12.0,3.1,5.0 =+ =+ = = 210)1( 2112/2)2( 10 00 1 0 2 12 1 2 1 0 0 2 2 xdxdxxxdx xxxdxxxdx xxdx x x x x x EB 8/1)5.0(5.0 = 1 2 3.1 3.121)3.1(13.1 2 FXP b 66.0)2.0()2.1(2.12.0 = FFXP sY ps = = 0,0 0, )( x xe xf x = c dxxf )(1cXPcXP = 1 = c dxxfdxxf 0 0 )()(1 = c x dxedx 0 0 01 2 1 = c e 2ln =c a 0q p X l H9 / q = ,0 1000, 1000 )( 2 x x xf CBv N0q M V | p | p v l H q NM m k V U p v l H x = 1500 )(1150011500 dxxfXPxP = 1500 1000 1000 )()(1 dxxfdxxf = 1500 1000 2 1000 1000 01 dx x dx 3 2 = 5 1012 = XPXPXP 41 1 5 50 0 5 3 1 3 2 3 1 3 2 1 = CC 243 232 a !$ Z 3 g HW X s9 V s q = 0 0 5 1 )( 5/ xe xf x $ Z8 HWV sL 7 C B1 Q p sQ q s$ ZB Q BQ T s s M m k s s Yq: 10= XA = 10 0 5/ 10 1 5 1 )(10)( dxedxxfXPAP x 2 e !$ ZB = sQ Y 1 p 1YP )1,5( 2 ebY 998.0)(1011 5)2( = eYPYP a ! p)2,3( 2 NX 1Y1Y 1 x 1Y D P 1YD1Y D =+ 3XP 31 XP 5.05.01 2 33 1 = = cXPcXP =Q cXPcXP =1 cXP = 21 cXP = 2 1 2 1 2 3 = c 30 2 3 = c c a 3 DN V = sb ? = b |B p q . ! X p q 12.005.1012.005.101 + XP + + = 06.0 05.1012.005.10 06.0 05.1012.005.10 1 + = 06.0 12.0 06.0 12.0 1 q q a 3 y ,0 0,0 43 yxke yx p 1Y Z sf b ! M k X Y q =),( yxf + ,0 20,10,3/ 2 yxxyx ppx+y1b != M X Y q =),( yxf = pH q b ,0 0 yxe y aa m != M X aY q = 0 ,10 2 3 ),( xyxxx yxf pH q 9 Q X aY M + = dyyxfxf X ),()( 10 x H )(xf X = + = 0 103 )( 2 xx xf X + = dxyxfyf Y ),()( 11 y H )1( 4 3 2 3 )( 2 1 | yxdxyf y Y = = 0 0)1( 4 3 )( 2 y yf Y = O 0 110)1( 4 9 )()( 22 yxyx yfxf YX A ),()()( YXfYfXf YX 2 3 2 3 ),( xxdydyyxf x x x x = + 1x 1 X Y M a ! XaYs? p X Y 1 2 1 1/6 1/3 2 1/9 3 1/18 a | H XY M $ 5 pHs p 9 2 = 9 1 = H X Y M a ! X aY M M O V ( sb k pZ L qs L 0 2 =Y+ Xxx 0 2 =+ YXxx 04 22 YX p 5 V AT= M 04 22 YXP X aY q9 5 p X aY q X = = 0 101 )( 0 101 )( x xf y yf XY X M Y = O 0 10101 )()(),( yx yfxfyxf YX = G dxdyyxfYXP ),(04 2 = 1 0 4/ 0 2 1 12 1 x G dydxdxdy a ! M M YXa X 01 ( s Y q =)(yf Y 00 0 2 2/ y y ye (1) p q YX 2 p1 =QZ 2 +2X +Y=0 L qb ( )1,0 UX 0, 0, b M Z= YX YX ,0 ,1 1Hq q 2 pZ s? pb EB M YXaQ = 0,0 0, )()( x xe xfyxf x XYX E= = 0,0 0, )( )( )()( )( ),( )( x xe xf yf yfxf yf yxf yxf x X Y YX Y YX YXPZP = 0 YXPZP =1 () = + ,0 0,0, ),( yxe yxf yx Q () dyedxYXP yx x + + = 00 () + = + dxee xx 1 0 + = YXPYXP 1 s p ; 1 + + a 05 p X l H9 q =)(xf 1000 100 100 2 x x x pBOLK P 150 l H 3 0519 q $3 50 9 q $ ! 3 05 p M 3 2100 150 150 2 = + dx x XP 05 p M N LM m L V U P l H105 n 27 8 3 1 3 2 3 03 3 3 = = CnP 27 1 3 1 3 2 0 30 0 3 = = CnP a ! M X s? p X 1 0 1 P k 0.3 0.4 0.3 p 12 2 += XY s pb 9 i : 1 :s p : 1 a ! M X s? p X 2 1 0 1 3 P k 1/5 1/6 1/3 1/15 11/30 pY =2 X 2 s pb :s p : 1 5 1 30 7 5 1 30 11 a ! p )10 X X eY = 12 2 += XY XY = q yYPyF Y =)( yeP X = H 0y 0)( =yF Y H0y )(yF Y )(lnln yFyxP = = 0 2 1 00 )( 2/)(ln 2 ye y y yf y Y yYPyF Y =)( yXP += 12 2 = = 2 1 2 1 2 1 2 1 y F y F y x y P XX 2 1 2 1 2 1 2 1 yy f yy f XX yYPyF Y =)( yxyP = () ( )yFyF XX = () ( )yfyf XX + = 0,0 0, 2 2 2 y ye y a ! * B M ( s _W N YV E h q b pW q 2 2IW = = ,0 119, 2 1 )( i if tIPtWPtF W = 2 2)( 2/2/ tItP = ()0 2 II F t F = v 0 0t ()= tf W 242162, 24 1 222 1 = t t t f t I 0 ()= tf W ,0 0, xe x pY=X 2 q b H0y =)(yF Y yXyPyXPyYP = 2 )(yF Y () ( ) 0 p X+Y q b = 00 0 )( x xe xf x X = 00 0 )( y ye yf y Y = = + 00 )( )( 2 z ze ee zf z zz YX = z xz z xzx z dxeedxezf 0 )( 0 )( )( : (X,Y) s = 000 0,0 ),( yx yxe yxf yx + = dxxzxfzf z ),()( Z=X+Y q f(x,z-x)d , u s YXa s q f = 0,0 0, )( x xe xf x 0 0 xz x xz x 0 p YX + # YX q b a M YXa )(),( 21 YX 5 )( 21 +YX )( )( 2 Y PY=j= 2 ! 2 e j j 1 ! 1 e k k X 1 PX=k= PX+Y=i= 7 X Y M = = i k i k kiYkXPkiYkXP 00 , U PX+Y=i= = = i k kiYPkXP 0 21 )!(! 2 0 1 = = e ki e k ki i k k !)!(! ! )( 2 0 1 21 i e kik i ki i k k + = = ! )( 0 21 21 i e C i k kikk i + = = )(21 21 ! )( + + = e i i i=0,1,2, # )( 21 +YX a sYV U 0q p l H9 i ! M OVBs q YXa YX = ,0 1000, 1000 )( 2 x x xf p Y X Z = q ! X V U05 p Y V U p l 05 () 8413.01 20 160 = 180 180 = 0 0 xz x xz x 0 )xz(f)x(f YX 0 0 0 zx x zx x 0 )zx(f)x(f YX H0z =)z(f Z zzx z x edxee + + = 2 1 H0z =)z(f Z zzxx edxee 2 1 0 = + + =)z(f Z z z z e z,e z,e = 2 1 0 2 1 0 2 1 a T =)z(f Z dy)y,yz(fy + d , 1000 1000 0 yz y x H 0z =)z(f Z H10 z =)z(f Z + 1000 dy)y(f)yz(yf 2 1000 222 2 110001000 z dy yzy y = +