概率论与数理统计答案

pXXXkkpp)1(pp−2)1(pp−1)1(−−kppXXXkpXXkpX)(xF}2{XP}31{≤XPFxPXxpkxxk(){}==∑X⎪⎪⎪⎩⎪⎪⎪⎨⎧≤≤≤≤==xxxxxxXPxF3,132,10/9215/3105/100}{)(2{2}3/PX=53{13}7/10PX≤=iX)2,1(=i)(xFi21)()(1+=xaFxFFx2()a121)()(1+=xaFxFFx2()2/1=a34433330123434XX012327/6427/649/641/64pkpXXXkkpp)1(pp−2)1(pp−kpp)1(−XXX0123Aii(,,=123)3iAAA12PAPAii()()==12(,,i=123)XX01231/21/41/81/8pkX⎪⎪⎪⎩⎪⎪⎪⎨⎧≤≤≤≤==xxxxxxXPxF3,132,8/7214/3102/100}{)(X2⎪⎩⎪⎨⎧≤≤=xxAxxxF1,110,0,0)(21A2X0.30.73XA231⎪⎩⎪⎨⎧≤≤=xxxxxF1,110,0,0)(22{0.30.7}0.4PX=3⎩⎨⎧≤=,010,2)(xxxfX⎪⎩⎪⎨⎧−=011)(2xxAxf1A2X)2121(−3XXAX2X1π/1=A3⎪⎩⎪⎨⎧≤−+−≤=1111arcsin2110)(xxxxxFπ231)21()21(}2121{=−−=−FFXPX⎩⎨⎧≤−=−0001)(xxexFx}2{≤XP}3{XPX21)2(}2{−−==eFXP3)3(1}3{−=−=eFXP2⎩⎨⎧≤=−000)(xxexfx3X⎪⎩⎪⎨⎧≤≤−=021210)(xxxxxfFx()XFxxxxxxxx()=≤≤−−≤⎧⎨⎪⎪⎪⎩⎪⎪⎪0012012121112222X)5,0(~UX5351}3{30==≤∫dxXP)2,10(~2NX}1310{XP}13{XP}2|10{|−XP}28{−XP}15{−XP{1013}0.4332PX={13}0.0668PX={|10|2}0.6826PX−={28}0PX−≈{1.5}1PX−≈X3200/)20(22401)(−−=xexfπ{||30}{3030}0.4931PXPX=−=Y3}30{XYY3B4931.0,~{1}0.8698PY≥=240~200)25220(~2NXα240~200β4240~2000.0642α=0.009β≈),(YX⎪⎩⎪⎨⎧+≤++−=22222222,0),(),(RyxRyxyxRAyxfA),(YX)(222Rrryx=+33RAπ={(,)}PXYD∈=2232(1)3rrRR−Y),(YX),(YX),(YXYXYYkp122XYXYXYYX12101/321/31/319)(YX⎩⎨⎧≤≤≤≤=,0,2010)(yxCyxf1C2)(YXXY5XY2/1=C2⎩⎨⎧≤=0,00,1)(xxxfX1/2,0()0,0Yyfyy⎧=⎨≤⎩XY20XY)3arctan)(2arctan(),(yCxBAyxF++=,xy−∞+∞ABCXY2π=C2π=B21π=A)9)(4(61),(),(2222yxyxyxFyxf++=∂∂∂=π,xy−∞+∞()Xfx=22(4)xπ+x−∞+∞()Yfy)9(32y+=πy−∞+∞XY⎩⎨⎧≤≤≤≤−=0010)2(8.4),(xyxxyyxfXY)(xfX)(yfYXYXY2-102-11)(xfX⎩⎨⎧≤≤−010)2(4.22xxx⎩⎨⎧≤≤+−=010)43(4.2)(2yyyyyfYYX⎩⎨⎧=0101),(xxyyxf)|(|yxfYX)|(|xyfXYYX62-172-19)|(|yxfYX)|(|xyfXYXYY10xx⎪⎩⎪⎨⎧=021)|(|xyxxyfXY10y⎪⎩⎪⎨⎧−=0111)|(|xyyyxfYX01≤−y⎪⎩⎪⎨⎧−+=0111)|(|xyyyxfYXYX)()(),(yfxfyxfYX≠YXbxa≤≤dyc≤≤YXYX⎪⎩⎪⎨⎧≤≤≤≤−−=,0,,))((1),(dycbxacdabyxf⎪⎩⎪⎨⎧≤≤−=,0,1)(bxaabxfX⎪⎩⎪⎨⎧≤≤−=,0,1)(dyccdyfY)()(),(yfxfyxfYX=YX),(~2σµNXσµ−=XY()Yfy22121ye−=π+∞∞−yXXP22+=XY13+=XY722+=XYYP13+=XYYP|)1,0(~NXXeY=|XY=⎪⎩⎪⎨⎧≤=−00021)(2/)(ln2yyeyyfyYπ()Yfy⎪⎩⎪⎨⎧≤=−00022/2yyeyπX;],8,1[,0,3/1)(32∈⎪⎩⎪⎨⎧=xxxf)(xFX)(XFY=Y)(xF)(XFY=)(XFY=)1)(0(≤≤XFy)(XFY=.1,10,0,1,,0)(≤≤⎪⎩⎪⎨⎧=yyyyyGXXNYN~()~()−1131XYZXY=−+27ZXYXN~(,)µσ112YN~(,)µσ222bYaXZ+=}10exp{101)(2zzf−=π()−∞+∞z8XY[02]}{YXP≤1{}2PXY≤=XYXYXYXY1y2y3y⋅==iipxXP}{1x2xjjpyYP⋅==}{XY1y2y3y⋅==iipxXP}{1x2xjjpyYP⋅==}{YX⎩⎨⎧≤=−0,00,)(xxxexxXϕ⎩⎨⎧≤=−0,00,)(yyyeyyYϕYXZ+=310()600zZezzfzz−⎧⎪=⎨⎪≤⎩∫∫+=zYXdxdyyxzF),()(ϕdxdyyexeyxxzz−−−∫∫=00YX⎩⎨⎧=+−,000,),()2(yxAeyxfyx1YXYX2YXZ2+=YX92=A1⎩⎨⎧≤=−0,00,)(xxexfxX⎩⎨⎧≤=−0,00,2)(2yyeyfyY)()(),(yfxfyxfYX⋅=YX2⎩⎨⎧≤=−000)(zzzezfzZ3321XX1X101012X1/41/21/41/21/2kpkp1}0{21==XXP11X2X21X2X1XX21X2X1X2X1X2X1X2X1X2XP2X011X-11/40001/221X2Xλ0TTTii()=123iTiftettTti(),,=≤⎧⎨⎩−λλ000FtettTti(),,=−≤⎧⎨⎩−1000λTTT=min{}123Tftettt(),,=≤⎧⎨⎩−30003λλ10XY}31,31:),{(≤≤≤≤=yxyxGYXU−=)(upXY⎩⎨⎧≤≤≤≤=,031,31,4/1),(yxyxf)}({)(+∞−∞=uuUPuFYXU−=0≤u0)(=uF2u1)(=uF20≤u∫∫−=uyxdxdyyxfuF),()(∫∫−=Guyxdxdy∩)(4122)2(411])2(4[41uu−−=−−=YXU−=⎪⎩⎪⎨⎧≤−=,020),2(21)(uuupXYXX01kp0.30.7yuxy=−32uyx−1uxy−=−123oxY)(yfYXU+=)(ugXY)(yFYXU+=}{)(uYXPuG+=}2{7.0}1{3.0=++=+XuYXPXuYXP}22{7.0}11{3.0=−+=−XuYPXuYPXY}2{7.0}1{3.0)(−≤+−≤=uYPuYPuG).2(7.0)1(3.0−+−uFuFU)2(7.0)1(3.0)()(−′+−′=′=uFuFuGug).2(7.0)1(3.0−+−ufuf11