Mathematica Engineering - Modelli e Metodi dell'Inferenza Statistica

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 /2ii KBbm`#BH2fp`B#BH2 H2iQ`B b2,(XPB)PA@BPF _2HxBQMB +QMi`QBKK;BMB@mMBQMB- BMi2`b2@xBQMB Q +QKTH2K2MixBQMB , X´1(BC)=( X´1(B))C X´1(Y!B!)= Y!X´1(B!) X´1(X!B!)= X!X´1(B!) S`Q##BHBi� /B mM BMi2`pHHQ , P((x, y ]) = F(y)´F(x) P([x, y ]) = F(y)´F(x´) P((x, y )) = F(y´)´F(x) P([x, y )) = F(y´)´F(x´) P(txu)= F(x)´F(x´) ZmMiBH2 /B Q`/BM2 !, #P(X"q!)#! P(X#q!)"1´! ñ #P(X"q!)#! P(X$q!)"! ñ #FX(q!)#! FX(qs!)"! .2}MBxBQM2 HBKbmT- HBKBM7 2/ 2b2KTBQ , liminf X n=HBK nÑ+8(inf m!nXm) limsupX n=HBK nÑ+8(sup m!nXm) A=
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� Ek=
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� A=limsupE n limsup =X8n=1 Yk"nEk P(Yk"nEk)=1 ´P(Xk"nECk) =1 ´P(HBKmÑ8 Xmk=nECk) =1 ´ HBKmÑ8 P(Xmk=nECk) =1 ´ HBKmÑ8 !mk=nP(ECk) =1 ´ HBKmÑ8 !mk=n56 =1 ´ HBKmÑ8 (56)m´(n´1)=1 P(A)= P(HBK bmT Ek)= P(X8n=1 Yk"nEk)=1 T2`+?� 2p2MiB /B T`Q##BHBi� R U Yk"nEk? T`Q@ ##BHBi� RVB=
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� B=XkPNEk P(B)= P(X8k=1Ek)= HBKnÑ8 P(Xnk=1Ek) = HBKnÑ8 !nk=1 P(Ek)= HBKnÑ8 (16)n=0 aTxB G , aB `B+Q`/ +?2 L12L2bQMQ bTxB p2iiQ`BHBXX:! Ñ Ro_ PL1ô E[X]PR xPL1%ñ | x|P L1 X, Y PLp2X [+= Y %ñ [X]=[ Y]PLp *m+?v@a+?r`x , X, Y PL2ñ| E[XY ]|" aE[X2]E[Y2] XPL2ñ E[X]2"E[X2] .Bbm;m;HBMx /B J`FQp , X o_ ñ P(|X|# a)" E[|X|] a @a&0 .Bbm;m;HBMx /B �2#v
p , XPL2o_ ñ P(|x´µ|# a)" Var (x) a2 G2KK /B 6iQm , aBMQ H2 o Xn2YiHB +?2 Xn#Y[+- YPL1X HHQ` E!HBK BM7n Xn""HBK BM7n E[Xn] hbbQ /B 7HHBK2MiQ , .iQ t&0, hX(t)= HBK"Ñ0+ P(t$X$t+"|X&t) " hX(t)= fx(t) 1´Fx(t) oHQ`2 ii2bQ 2 KQK2MiBoHQ`2 ii2bQ , E[h(X)] = "!h(X(#))I(d#) ="!h(X(#))P(d#)= "Rh(x)PX(/x) ="Rh(x)fX(x)/x L2H +bQ /Bb+`2iQ, E[h(x)] = #kh(xk)pk o`BMx 2 +Qp`BMx , Var (X)= $2X=E[X2]´E[X]2- Cov (X, Y )= $XY =E[XY ]´E[X]E[Y] Var (X+Y)= Var (X)+ Var (Y)+2 ¨Cov (X, Y ) aB MQiB +?2 M2H +bQ KmHiB/BK2MbBQMH2 H p`BM@ x /Bp2Mi H Ki`B+2 C /Qp2 ;HB 2H2K2MiB bmHH /B;QMH2 bQMQ B $2Xi2 [m2HHB 7mQ`B $XiXjX *Q2{+B2Mi2 /B +Q``2HxBQM2 HBM2`2 , %= Cov (X, Y ) aVax (X)Var (Y) h`b7Q`KxBQMB {MB , .iQ Y=AX +b, E[Y]= AE[X]+ b, Var [Y]= AV ar [X]AT=CY=AC XAT o2iiQ`B H2iQ`Bo2iiQ`B H2iQ`B , aB X p2iiQ`2 H2iQ`BQ, E[h(X)] = "!h(X)dP="Rnh(x)dP X = ##xPSh(x)p(x) X
 /Bb+`2iQ "Rnh(x)f(x)/xX
 +QMiBMmQ S2` +H+QH`2 H 7mMxBQM2 /B `BT`iBxBQM2 /B mMp`B#BH2 bT2+B}+,*QMiBMmQ , fk(xk)= "f(x1,...,n )/x1... /xk´1/xk+1 ... /xn UBMi2;`H2 bm imii2 H2 +QKTQM2MiB +?2 MQM +B BM@i2`2bbMQ- Qpp2`Q imii2 i`MM2 xkV .Bb+`2iQ , ;HB BMi2;`HB /Bp2MiMQ bQKKiQ`B2X s
 mM p2iiX HX +QMiBMmQ b2 *
 BMp2`iB#BH2Xh`b7Q`KxBQM2 p2iiX HX +QMiBMmQ aB (X, Y ):! Ñ R2p2iiX HX +QMiBMmQ +QM /2MbBi� f(X,Y )X AH bmTTQ`iQ /B P(X,Y )
S!R2 (U, V )= h((X, Y )) = ( h1(X, Y ),h2(X, Y )) +QM h:R2Ñ R2 a2 hPC1(S)-det (Jh)(x, y )‰02 Dg=h´1,g :h(S)Ñ S +QM g(u, v )=( g1(u, v ),g2(u, v )) HHQ` (U, V )
 mM p2iiX HX +QMiBMmQ 2 f(U,V )(u, v ) =fX,Y (g1(u, v ),g2(u, v ))|det (Jg)(u, v )| o2iiQ`B H2iQ`B ;mbbBMB.iQ X=( X1,...,X n)„N(µ, C ) /Qp2 µPRn,C PRnˆn,C &0- HHQ` Tm
� M+?2 2bb2`2 /2}MBiQ +QK2,&(X1...n )(u)= 2tT ti$u|µ&´ 12$u|Cu &u %ñ$ a|X&„ N @aPRn ZmBM/B fX(x)= 1 a(2')ndet (C)2tT "1 2$x´µ|C´1(x´µ)& * S`QT`B2i� , RX Xk„N(µk,Ckk) kX SX=Im (C)+ µ=Col (C)+ µ =[ Ker (C)]K+µ jX X *QMiBMmQ ô det (C)‰0ô C&0 9X APRnˆn,bPRn ùñ AX +b„N(Aµ +b, AC A T) 8X XiKK Xj%ñ Cov (Xi,X j)=0 h`b7Q`KxBQMB {MB , Y=AX +b, Y „N(Aµ +b, AC A T) X„N(µX,$2X)-Y„N(µY,$2Y)- aX +bY „ N(aµX +bµY,a2$2X +b2$2Y+ 2ab$ XY ) . p2`B}+`2, a2$2X+b2$2Y+2 ab$ XY #0 *bQ #B/BK2MbBQMH2 , #X Y $ „N %# µX µY $ , # $2X Cov (X, Y ) Cov (X, Y ) $2Y $& &(X,Y )(u, v )= 2tT !i(µXu+µYu)´ ´12(u2$2X+2 Cov (X, Y )uv +v2$2Y)) AM [m2biQ +bQ H T`QT`B2i� UjV Tm
� M+?2 2bb2`22bT`2bb +QK2,#X Y $ ô det (C)‰0ô $’& ’% $X&0 $Y&0 |%X,Y |$1 f(X,Y )(x, y )= 1 2#$X$Yb1´%2(X,Y )¨ ¨2tT # 1 2(1 ´%(X,Y )) !(x´µX)2 $2X + ´2¨%(X,Y )(X´µX)(y´µY) $X$Y +(y´µy)2 $2Y "+ 6mMxBQMB +`ii2`BbiB+?26mMxBQM2 +`ii2`BbiB+ , 6mMxBQM2 +QKTH2bb BM +Q``BbTQM/2Mx #BmMBpQ++QM H H2;;2- H [mH2
 / 2bb +`ii2`BxxiX&X(u)= "Rnei#u|X!PX(/x)= E[ei#u|X!]= "!ei#u|X!dP 6mMxBQM2 +`ii2`BbiB+ 2 KQK2MiB , Bm Buk1¨¨¨B ukm &(0) = imE[Xk1¨¨¨ Xkm ] E[Xk]= 1 i B&(0) Buk E[X2k]= ´B2&(0) Bu2k -E[XkXj]= ´B2&(0) BukBuj h`b7Q`KxBQMB {MB , .iQ Y=AX +b, &Y(u)= eixu|by&X(ATu) S`Q#X 2 H2;;B +QM/BxBQMi2S`Q##BHBi� +QM/BxBQMi , P(A|B)= P(A, B ) P(B) P(A)= #nP(AXEn)= #nP(A|En)P(En) 6Q`KmH /B "v2b , P(Ek|A)= P(A|Ek)P(Ek) #nP(A|En)P(En) G2;;B +QM/BxBQMi2 , Y|X=x„fY|X(‚|x) f(X,Y )(x, y )= f(Y|X)(y, x )¨fX(x) E[Y|X=x]= m(x)= "SYyfY|X(y, x )dy Var (Y|X=x)= q2(x) ="SY(y´m(x))2fY|X(y, x )dy L2H +bQ /B o /Bb+`2i2
 bm{+B2Mi2 bQbiBimB`2 P / f2 bpQH;2`2 ;HB BMi2;`HB +QK2 bQKKiQ`B2X oHQ`2 ii2bQ +QM/BxBQMiQ , a2 YPL1HHQ` E[Y]= E[E[Y|X]] o`BMx +QM/BxBQMi , Var (Y|X)= E[Y2|X]´E[Y|X]2 Var (Y)= Var (E[Y|X]) + E[Var (Y|X)] o2iiQ`B :mbbBMB +QM/BxBQMiB k@/BK , X„N(µX,$X)-Y„N(µY,$Y) #X Y $ „N %# µX µY $ , # $2X %$X$Y %$X$Y $2Y $& $X=0 ùñ X„N(µX,0) = (µX ùñ P(X=µX)=1 ùñ Y|X=µX„Y„N(µY,$2Y) $X&0ùñ Y|X=s„N(m(s),q2) m(s)= µY+cov (X,Y ) var (X)(s´µX)= µY+%$Y$X(s´ µX) var (Y|X = s)= q2= var (Y)´ cov (X,Y )2 var (X) = $2Y(1´%2) o2iiQ`B :mbbBMB +QM/BxBQMiB M@/BK , X„N(µX,CX)M@/BK- Y„N(µY,CY)K@/BK, #X Y $ „N %# µX µY $ , #CX CXY CYX CY $& det (CX)&0ùñ Y|X=s„N(m(s),Q ) m(s)= E[Y|X=s]= µY+CYX C´1X (s´µX) Q=var (Y|X=s)= CY´CYX C´1X CXY .Bbi`B#mxBQMB.2Hi /B .B`+ U(nV, P(X=n)=1 &(u)= einu *QMiBMm mMB7Q`K2 UU(a, b )V, f(x)= 1 b´a1(a,b)(x) F(x)= x´a b´a E[X]= a+b 2 ,Var [X]= (b´a)2 12 &(u)= eia+b2usin 'b´a 2 u ( / 'b´a 2 u ( +QM ´8$ a$b$+8. "2`MQmHHB UBe (p)V, JBbm` H
�2bBiQ /B mM 2bT2`B@ K2MiQ p2`Q@7HbQBe (p)ô &X(u)= peiu+1 ´p, +QM pP[0,1]. E[X]= p-Var [X]= p(1´p) "BMQKBH2 UBi(n, p )V, aQKK /B M Bi(p)X amT@ TQ`iQ, t0,1,2,... u P(X=k)= )nk*pk(1´p)n´k,)nk*= n! k!(n´k)! E[X]= np V ar [X]= np(1´p) R 6m#BMB bhQM2HHB @ TTmMiB /B T`Q##BHBi� @ 7m#BMBiQM2HHBXBi Bi(n, p )ô &(u)=( peiu+1 ´p)n, +QM pP[0,1]2nPN. :2QK2i`B+ UG(p)V, LmK2`Q /B 7HHBK2MiB T`B@ K /B mM bm++2bbQ BM mM T`Q+2bbQ /B "2`MQmHHBXS`Bp /B K2KQ`BX amTTQ`iQ, t1,2,3... u P(X =k)= p(1´p)k´1 F(k)= P(X "k)= 1´P(X#k+1) = 1 ´(1´p)k E[X]= 1p Var [X]= 1´pp2 G(p)ô &(u)= peiu 1´eiu(1´p). :2QK2i`B+ i`bHi , P(W =k)= p(1´p)k AT2`;2QK2i`B+ UH(n, h, r )V, .2b+`Bp2 H
�2bi`xBQM2 b2Mx `2BKKBbbBQM2 /B THHBM2 /mM
�m`M +QM M THHBM2 /B +mB ` /2H iBTQ s 2 M@`/2H iBTQ uX G T`Q##BHBi� /B Qii2M2`2 F THHBM2/2H iBTQ s 2bi`2M/QM2 ? /HH
�m`M
 P(X=k)= )hk*)n´hr´k* )nr* T2` max t0,n ´N2u" k"min tn, N 1u E[X]= rhn Var [X]= h(n´h)r(n´r) n2(n´1) SQBbbQM UP0())V, G2;;2 /2;HB 2p2MiB ``BX GB@ KBi2 /2HH2 /Bbi`B#mxBQMB #BMQKBHB +QM )= npX amTTQ`iQ, t0,1,2,... u P(X=k)= e´&&kk! E[X]= )Var [X]= ) P0()),) &0ô &(u)= 2tT t)(eiu´1)u LQ`KH2 UN(µ,$ 2)V, f(x)= 1 ?2'$ 22tT " ´(x´µ)2 2$2 * E[X]= µVar [X]= $2 E[(X´µ)4]=3 $4 P(x"t)= P 'X´µ $ " t´µ $ ( =P ' Z" t´µ $ ( +QM Z= X´µ $ „N(0,1) N(µ,$ 2)ô &(u)2tT !iuµ ´$22u2) GQ;MQ`KH2 Ulog N(µ,$ 2)V,X=eN f(x)= 1 x?2'$ 22tT " ´(lnx ´µ)2 2$2 * 1(0,+8) F(x)=" (µ,$ )(lnx ) E[X]= eµ+$2/2 Var [X]= e2µ+$2(e$2´1) *?B@[m/`Q U*2(k)V, aQKK /B F N(0,1) H [m/`iQX f(x)= 1 2k/2#(k/2) xk/2´1e´x/21(0,+8) E[X]= kVar [X]=2 k *2(n)=#( n2,12) *2(k)ô &(u)=(1 ´2iu)´k2 h /B aim/2Mi UT(n)V, T=Z/bQn,Z „N(0,1),Q „*2(n),Z KK Q f(x)= "(n+12) "(n2)?#n ¨ 1 (1+ x2n)n+12 E[T]=0 b2n&1QTTm`2 BM/2}MBiQX Var (T)= n n´2b2n&2QTTm`2 BM/2}MBiX 1bTQM2MxBH2 UE())V, .m`i /B pBi /B mM 72MQK2MQX S`Bp /B K2KQ`BX )&0X f(x)= )e´&x1(0,+8)(x) F(x)=1 ´e´&x E[X]= 1&,Var [X]= 1&2,E())ô &(u)= &&´iu :KK U#(!,) )V, bQKK /B o BM/BT2M/2MiB +QM /BbiX 2bTQM2MxBH2X )&0,! &0X f(x)= )!x!´1e´&x #(!) 1(0,+8)(x) F(x)= ' 1´!´1# k=0 e´&x ()x)k k! ( = +(!,)x ) #(!) +QM xP[0,+8)2!BMi2`QX #(!)= "80x!´1e´x/x #(!+1) = !#(!)#( n+1) = n! #(1) = 1 ,#(12)= ?', E[X]= !&,Var [X]= !&2 Z2„#(12,12)= *2(1) E[Xk]= !(!+1) ... (!+k´1) )k +QM kPZ,! +k&0 Y=cX „#(!, &c)+QM c&0,X „#(!,) ) #(!,) )ô &(u)= ' ) )´iu (! q2B#mHH UW(), k )V,)&0,k &0X f(x)= k )kxk´1e´(x/&)k1(0,+8)(x) F(x)= e´(x!)k,E[X]= &k#(1k), Var [X]= )2 k2[2k#(2k)´#2(1k)] AKTQM2M/Q F4R
 mM
�2bTQM2MxBH2X *m+?v UC(x0,y0)V, f(x)= 1 ' y0 (x´x0)2+y20 F(x)= 1 'arccot 'x0´x y0 ( C(x0,y0)ô &(u)= eix0u´y0|u| G /Bbi`B#mxBQM2 /B *m+?v MQM ? M� pHQ`2ii2bQ M� p`BMxX *QMp2`;2Mx /B o*QMp2`;2Mx KQMQiQM , aBMQ H2 o Xn2XiHB +?2 0"Xn"+8,X nÒ X [+- HHQ`, E[Xn]n'Ñ E[X]- +BQ� E!HBKnXn"=HBKnE[Xn]X *QMp2`;2Mx /QKBMi , aBMQ H2 o_ Xn,X,Y iHB +?2 Xn qc'Ñ X-|Xn|" Y [+ @n-YPL1- HHQ`, XnPL1-XPL1-E[Xn]n'Ñ E[X]X *2`i , aBKBH2 / mM +QMp2`;2Mx TmMimH2- XnÑ X @#P! ZmbB +2`i ,P(XnÑ X)=1 Qpp2`Q A=( XnÑ X)PA2P(A)=1 Zm2biQ bB;MB}+ +?2 H +QMpX pH2  K2MQ /BBMbB2KB /B KBbm` MmHHX L2;HB bTxB Gp,XnLp'Ñ X b2 XnPLp@n-XPLp2E[|Xn´X|p]Ñ 0 .iQ p#q#1- +QMpX BM Lpñ +QMpX BM LqX *QMp2`;QMQ B KQK2MiB, E[|Xn|p]Lp''Ñ E[|X|p] S2` p=1 2p=2 , E[Xn]Ñ E[X]2 Var (Xn)Ñ Var (X) S`Q##BHBi� ,Xn P'Ñ X b2 @,&0P(|Xn´X|&,)Ñ 0 1bBbi2 mM bQiiQbm++2bbBQM2 /B Xn+?2 +QMp2`;2 [X+X  XX a2 X TT`iB2M2  Lp2/
 TQbbB#BH2 i`Qp`2 mM Y iH2 +?2 |Xn|"Y HHQ` [m2bi +QMp2`;2 M+?2 BM LpX .2#QH2 , aBMQ Pn2PT`Q# bm (R,B)X HHQ` Pndeb'Ñ Pb2"RhdPnÑ "RhdP@h+QMiX 2 HBKX AM H2;;2 Q /Bbi`B#mxBQM2 ,Xn L'Ñ X b2 PXndeb'Ñ PX aHmibFv, Xn L'Ñ cñ Xn P'Ñ c *`Bi2`B +QMpX BM H2;;2 , Xn L'Ñ X ô Fn(s)Ñ F(s)@sPS/Qp2 F
 +QMiX.Bb+`2iQ ,P(Xn= s)Ñ P(X = s)@sPSô Xn L'Ñ X /Qp2 S=SXYSXn *QMiBMmQ ,fn qo'Ñ fñ Xn L'Ñ X G2pv U;2M2`B+QV, Xn L'Ñ Xñ &nÑ & &nÑ &2&+QMiX BM y ñ Xn L'Ñ X _2HxBQM2 i` H2 +QMp2`;2Mx2 , S`QT`B2i� , a2 XnÑ X 2YnÑ Y- HHQ`  b2+QM/ /HH +QMp2`;2Mx TQbbQMQ pH2`2 H+mM2 Q imii2 H2b2;m2MiB T`QT`B2i�,R, aX nÑ aX U[+- Lp-P-LV k, h(Xn)Ñ h(X)U[+- P-LV j, Xn+YnÑ X+YU[+- Lp-PV 9, XnYnÑ XY U[+- PV 8, Y, Y n‰0@# ùñ Xn YnÑ X Y U[+- PV a2 Y +QMp2`;2  mM +QbiMi2 BM H2;;2 pH;QMQ M+?2 H j- 9 2 8 Ui2Q`2K /B aHmibFvV G:L , .iB XnPL1BB/ 2 µPR- HHQ` E[Xn]= µ%ñ sXn qc'Ñ µ2sXnL1'Ñ µ h*G , .iB XnPL2BB/- µ=E[Xn]- $2=Var (Xn)&0- HHQ`, (sXn´µ)/+$?n , L'Ñ N(0,1)X o2HQ+Bi� /B +QMp2`;2Mx ,Xn+QMp2`;2 p2`bQ a+QM p2HX vnb2, vn(Xn´a)L'Ñ T(„(0X bBMiQiB+ MQ`KHBi� , a2 T „ N(0,q)- +QM q&0HHQ`, Xn„AN (a, q /v2n) J2iQ/Q .2Hi R , a2 vn(Xn´a)L'Ñ THHQ`, vn(h(Xn)´h(a)) L'Ñ h1(a)¨T- /Qp2 im (Xn)) B-B #Q`2HBMQ /B R-aP˚B UTiQX BMi2`MQV- h:BÑ R#Q`2HBM 2 /BzX BM aX L2H +bQ bBMiQiX MQ`KH2, Xn„AN (a, q /v2n) ñ h(Xn)„AN +h(a),(h1(a))2q v2n , _BbmHiiB MQi2pQHBJ2/B +KTBQM`B ,sXn= 1n#nk=1 Xk R, E-sXn.=µ @nU+Q``2ii2xxV k, Var (sXn)= $2n n'Ñ 0UQpp2`Q sXnL2'Ñ µV j, sXn qc'Ñ µT2` H G:L U+QMbBbi2MxV 9, sXn´µ $/?n L'Ñ N(0,1) T2` BH h*GX o`BMx +KTBQM`B , S2n= 1n´1#nk=1(Xk´ sXn)2 R, E-S2n.=$2 @nU+Q``2iiQVX j, S2n qc'Ñ $2U+QMbBbi2Mi2VX 9, (S2n´$2)/ 'bµ4´$4n ( L'Ñ N(0,1) Qpp2`Q S2n„AN ($2,µ4´$4n )- /Qp2 µ4=E-(Xn´µ)4.‰$4X aiBK /B mM T`QTQ`xBQM2 , U+Q``X 2 +QMbBbiXV ppn= 1n#nk=1 1B(Xk) (ppn´p)/ 'bp(1´p) n ( L'Ñ N(0,1) T2` BH h*GX aiBK /2HH 6 /B `BT`iX , U+Q``X 2 +QMbBbiXV Fn(t)= 1n#nk=1 1(´8 ,t)(Xk) = 1n#nk=1 1[Xk,+8)(t) BM [mMiQ Xk"tô t#Xk Fn(t)„AN +F(t),F(t)(1´F(t)) n , S`Q/QiiQ /B +QMpQHmxBQM2 , Y=X1+X2,P Y=PX1˚PX2 fY(t)=( fX1˚fX2)(t)= "RfX1(y´t)fX2(t)dt aQKK /B /Bbi`B#mxBQMB , "2`MQmH HBM2 ,X1,...,X n„Be (p)BM/BTX ùñ X1+¨¨¨ +Xn„Bi(n, p ). :mbbBM2 ,X1,...,X n„N(0,1) BM/BTX ùñ X1+¨¨¨ +Xn„N(0,n). ùñ X21+¨¨¨ +X2n„*2(n). 1bTQM2MxBHB ,X1,...,X n„E())BM/BTX ùñ X1+¨¨¨ +Xn„#(n,) ). :KK ,X„#(!,) ),Y „#(-,) )BM/BTX ùñ X+Y„#(!+-,) ). SQBbbQM ,X„Po ()X),Y „Po ()Y)BM/BTX ùñ X+Y„Po ()X+)Y). a2`B2 , #8k=0 qk= 1 1´q,|q|$ 1 #Nk=0 qk= 1´qN+1 1´q ,|q|$ 1 ex=HBK nÑ+8(1 + xn)n=#8k=0 xk k! #ni=1 i= n(n+1) 2 #ni=1 i2= n(n+1)(2 n+1) 6 #8i=1 i´s=!pprimo 1 1´p´s=.(s) #8n=1(´1)nxn= 1 1+ x,|x|$ 1 #8i=1 xi i=HM ' 1 1´x ( ,|x|" 1,x ‰1 k 6m#BMB bhQM2HHB @ TTmMiB /B T`Q##BHBi� @ 7m#BMBiQM2HHBXBi