deug2 probabilité

52
EQUIPE D’ANALYSE ESA 7064 – CNRS Universit ´ e Pierre et Marie Curie - Paris 6 Tour 46 - 0 - Boˆ ıte 186 - 4, place Jussieu - 75252 PARIS CEDEX 05 el : (33-1) 44 27 53 49 - el´ ecopie : (33-1) 44 27 25 55 - [email protected] COURS DE MA THEMA TIQ UES DEUG 2 Pr obabilit ´ es et Statistique Sylvie DELABRIERE

Upload: john3021

Post on 21-Nov-2015

233 views

Category:

Documents


3 download

DESCRIPTION

cours de probabilités DEUG 2

TRANSCRIPT

  • EQUIPE DANALYSEESA 7064 CNRS

    Universite Pierre et Marie Curie - Paris 6

    Tour 46 - 0 - Bote 186 - 4, place Jussieu - 75252 PARIS CEDEX 05Tel : (33-1) 44 27 53 49 - Telecopie : (33-1) 44 27 25 55 - [email protected]

    COURS DE MATHEMATIQUES

    DEUG 2

    Probabilites et Statistique

    Sylvie DELABRIERE

  • ! " #$%! "& '! "( )

    *,+* -/.10243%5%68792;:A@CBEDGF,HE@IHEJ>JA5LK2NM

    OQPRPTS=USWVGXQUZY[QUT\^]SW_`ab\QcbS=dZY[eY\efRgahcSW[iXjfe`PZklabcbcbVG[i`ab\iSmfeS=_`VGcb`ah\jfQ]S8XiSW\in1ahPTSW\Go$SWp4YkXiSWn1SWP%XiqrcbS

    k`n1U`\iXAS8n1SWP%XsfGt VGPuUGdj]S8PG`nNvSWPGSwYc]SxYXi`ah\iS%yIz{Sw|8VZt `PuUSWVGXj}AYab\iSx~UZY\sk`PxXi\iSx~lkWt SW[iXjSW[i[YiS8\sfS

    f]SWYSW\jfGt VGPRUGdj]SWPG`nNvS8PGS=VGPTSmkSW\iXeYahPTSmk`PZfeVTahXiS=SWPn1`eS8PGPGS%~SWPR}\^]Sx|8VGSWP{kS SWXjY1\insSW\j|WVGS=XiSWc

    ]SW_=]S8PGSWn1S8PxXY1TQT=feSj[SjUT\i`^feVTab\iSxy4zt S8[iXaka4cYEPT`XAab`PfSjUT\i`{YGabchabX^]Sxy

    SWVGpU`abPxXi[feSj_%VGS[i`P%X

  • 8b ! " #"b! "& '! "( )

    *,+ DGF,HE@IHEJ>AJ5LK2?3%.ED.E23%B=@l7^2?=EJ+

    `VG[[iVTUGU`[iSW\i`PT[

    VG[e|8VZtbvY=cY=TPfSskSRkd{YUTahXi\iSR|WVTSct S8[iUZYkSRSW[iX

  • ! " #$%! "& '! "( )

    /

    %{Z8 FHG

    Gr{ieebhxeW WGWh

    ?>

    8

    W8

    >A@

    WLbGGj8GJI

    Gei8

    B

    8

    KB

    W8

    KB

    @9&L

    W

    @

    WhL4e

    @

    ;=A@

    KB

    ;

    I

    7G

    "

    IWTW1W4TS^EZieebbxWe{TTWZ

    #"

    ,VU

    "

    U

    I

    VU

    "

    U

    U

    U

    /

    x0!1324{ WX

    GuW W%WEZb;

    Y

    1h8uW8s8ih8GWW^Wbh48W%4eiTl4WWG

    e^QWW^bWLW{WW

    i4ZeGbLGjWW4eRQ!ZiehbxW^e%{ib4eW1W4{GTGR

    G8W NjR

    ?

    WWWWmZB

    ;

    G8WeWW8iib{GjTxejW

    ?

    8WWWs[B

    ;

    {bGhTWWiLee8WWih GZWW

    ;

    Ws[B

    ;

    t]Sx|WVTa

    UG\i`ZYGabcbahX^]SP{t S8[iXNUZY[NcY[iSWVTchSuUG\i`ZYGabcbahX^]S|WVGSuct `P\iS8PZk`P%XA\iSuUG\eYXia|8VGSWnsSWPxXN[iVT\NcbSW[

    SWPG[SWnGcbSW[LGPTah[g4fGYPG[LchSkWY[fTt VTPfQ]SjUTahUj]Sx~%`PNUSWVTXYi_`ab\

    B

    8

    B

    B\

    B]

    B

    KB^

    *,+`_ aw@lDGJ@IHE>23@I>9K2@I5xFJDG2433%.ED.E243"B=@l792cb=2;B=DGF,HE@lH=JA>J5=K2?E=J+

    d

    VcbahS8VfSr[et abPxX^]SW\iS8[i[iS8\mfeab\iSxkXiSWn1S8PxXmvYjct]SW_=]SWPGSWnsSWPxXmYc]SxYXi`ah\iSx~G`P_GYj[et `4kWkVGU9SW\mfeS[eYjcbSxkXAVT\iSvY

    XA\eYi_S8\i[VGPSWS8X|WV{t abc,UG\i`4feVGabXey,zt S8[iXVGPUSWVcYneSWn1SfQ]SWnY\ekdTS|8VGa,[iVTahXg,|8VGS8c|8VZt VGP |WVTa,[iS

    chS8_GYP%XEcbSnYXiahPS8XE_`VGcYPxXsk`PGPZY3e

    f

    Xi\iScYrXiSWn1U]SW\eYXiVG\iSS8pxX^]SW\iabSWVT\iSx~TcbabXE[i`PXidGS8\in1`nvS8XA\iSUTchVTX!e`X

    |WVTSfSN[`\iXiab\eyhgc[etbYahXscvYufScYPT`XAab`P}`PZfTYn1S8PxXeYcbSfV;k8YckVTcfeSW[sUT\i`{YGabchabX^]SW[gkSWcbcbSfV

    XA\eYPT[iU`\iXfeVdZY[eY\efGy

  • 8b ! " #"b! "& '! "( )

    /

    %{Z8wi

    Gl8hbjiibhWhjk

    Wr^%l

    8

    >

    l->

    8

    .p>

    {bGhTWWiLee8WWih GZWWqsr1iZ ^WW4ZbhxE8%

    o

    $GijTt$WEGW^u

    o

    >

    8

    >

    >

    \

    >

    ]

    >

    ,

    ;=

    ;

    YPG[ct S8pxS8n1UGcbS

    ~

    o

    SW[iXvYs_GYcbSWVT\i[fGYPT[

    n

    W

    bh

    W

    SWXfGYPG[mct SWp%SWn1UGcbS

    ~

    o

    SW[XNvY

    _GYcbSWVT\i[fTYPT[

    n

    ?

    W

    bb

    8

    y

    *,+`v wF,JJb10.EE2+xZ@lDGJ@IHE>A2?@I>9K24@I5%F,JDG2?3%.ED.E243"B=@l792cb=2;B=DGF,HE@lH=JA>J5=K2?E=J+

    zt S8[iXaka4cYE_=]SW\iabXeYTchSPG`Xiab`P feSXA\eYPT[iU`\iXey

    e`ahX

    fe`PTP]SjS8X

    o

    gGL

    n

    VTPGS_GY\iaYGcbSYc]SxYXi`ah\iS%y

    OQPU`[iSR??>

    8

    W8

    >A@

    S8X

    n

    ??y

    8

    8WKy

    9

    ]SWGPTah[[i`PG[mz

    ;

    o

    -y

    ;

    ,

    ?>{&

    o

    >L,-y

    ;

    l

    o}|

    8

    ?y

    ;

    OQP\iSWnY\e|WVTS

    9

    ;=L,-y

    ;

    UTVGab[e|8VGSRkSj[`P%XfeSW[LSWPT[iSWnTchS8[fah[

    `ahP%Xi[e

    ?

    l

    `PZk

    z

    8

    WW

    z

    9

    f]SWTPGabXVGPGSUG\i`ZYGabcbahX^]S[iVG\

    n

    y

    /

    %{Z8

    1GlWbb

  • ! " #$%! "& '! "( )

    LW%WEZbW

    h

    ,

    o

    |

    8

    il?

    W

    W

    l

    4{%^%{xs,1eN0G48{w

    ZZ1e{4{Z{0u130TL%N1e

    B

    zt S8[iXcYEcb`aQfGt VGPTSj_GY\iaYTchSYc]S%YXi`ab\iS

    o

    UG\iSWP{YPxXfeS8VGp_GYchS8VG\i[ESWX

    Yi_Sxk

    o

    l

    B

    o

    ,

    B

    ZZ60T

    /

    %{Z8 6

    7GbW4[I

    &Z

    %

    -

    B

    ubh1bbA

    IKB

    WEhub

  • 8b ! " #"b! "& '! "( )

    %0TW5

    7T

    j

    e8ZWRT{ieebbx

    7G

    "

    x$ ^Gx WG81W^i

    ZW8^bNlR

    #"

    %$

    ,

    #"-(

    $

    )

    uN'!6

    g

    OQPC]Sxk\iahX

    n

    z

    o

    .pN,

    ;

    zy

    ;

    .

    i

    o

    -y

    ;

    )

    ,

    ;

    zuy

    ;

    o

    -y

    ;

    -

    .

    ;

    o

    -y

    ;

    )

    ,

    ;

    zy

    ;

    o

    -y

    ;

    .

    -

    l+z

    n

    o

    .p

    n

    N

    SW[LUG\i`U`[iabXAab`PG[

    SWX

    [i`PxXabn1n]SxfaYXiSW[y

    YEUG\i`U`[iabXiah`P-

    SW[iXVTPGSRk`PT[^]Sx|8VGS8PZkSchSct abP]SWYcbahX^]SXA\iaYPGVGcYab\iSRg

    @

    ;=

    l->

    8

    .p>

    bi

    n

    o

    l

    .

    .

    .

    .

    .

    .

    .

    .

    .

    .

    x

    Y\

    o

    l

    .

    .

    .

    .

    .

    .

    .

    .

    .

    .

    {bGhTWWiLee8WWih GZWWqsr1iZ ^WW4ZbhxE8%

  • ! " #$%! "& '! "( )

    o

    GijT~WEGW^u

    o

    >

    8

    >

    >

    \

    >

    ]

    >

    ,

    ;=

    ;

    bi

    n

    o

    ,

    .

    8

    .

    .

    ]

    .

    ]

    .

    W

    x

    Y\

    o

    l

    8

    .

    W

    8

    .

    W

    .

    8

    ]

    .

    W

    ]

    .

    W

    0T{0ZZ1e{4{%Z0uZZ0G

    Z{1eZ4ZZ{wh0u130TL%%1e

    B

    OQP_L]S8\iahTSR|8VGSRg

    n

    o

    ,

    Y\

    o

    ,

    B

    .

    :

    B

    ZZ60T

    OQP_L]S8\iahTSRfeSneSWn1S|WVTSRg

    n

    o

    ,

    @

    ;=

    o

    >=l-y@

    jNMGGeTQZihbxhCeW 8ZW

  • $ b! '!!

    /

    %{Z85

    TlWbbjTxhG^ZebNixWWu1biibebjWhi

    o

    ibxiTT

    n

    4b1Txhp

    %MTGbQZ

    yt&

    '

    y{,

    o

    yI

    SW[QUG\i`UG\a]SWX ]^SW[Q[VGab_GYP%XiSW[jfeS8[}`PZkXiab`PT[jfeS=\^]SWUZY\iXiabXAab`PfeS=_^yYyfeab[ek\WvSWXiS8[[`P%XfSW[jk`PG[4]S%|WVTSWPZkSW[

    ahn1n ]S%feaYXiSW[feScYsf]SWGPTabXAab`Pg

    1e,8W6F

    7T

    o

    eT~

    ThWxxuibxeiLGG

    n

    ;?y

    8

    y

    bb

    y@

    b

    x

    i'C1G%bNTj^{eb

    1Gxbp'CW{WN8iWbh8e

    1Gxbp'CW{Wihi^x{WEZibiW4ir1x

    cbahn

    yIl

    cbahn

    |

    yIl !

    E+`_ N3%BK24DG@l=7^2+b10.EE2+xr+@=+`bEJ3%7^D'245%2Q+

    `VG[uYcbcb`PT[

  • 8b ! A'!!

    1eh1e

    %

    %1

    n

    z

    o

    .N,z

    n

    o

    .p

    n

    N

    bhjWix%

    7G

    o

    n

    o

    7G

    o

    %

    n

    o

    l?

    o

    ?

    s

    n

    U

    o

    U

    U

    n

    o

    U

    `aka4VGPGSUG\i`UG\ia]SWX^]SSW[i[iS8PxXiabSWcbchSfeSct SW[U]SW\eYPZkSRg

    1e,8W{5

    7T

    o

    eTiibhLWhi~ibxeiGG

    n

    %eGLTZbh8b

    G

    n

    GG

    liij8

    hiL

    n

    o

    9

  • $ b! '!!

    8hTW11W4

    n

    o

    @

    l

    9

    y

    @

    9

    B

    9

    iibGWG

    o

    W{%MTGbji

    o

    G1xN11W4{&

    "

    >=l E[a'>

    &

    "

    /

    x0!1324{w6

    7T

    "

    bi

    #"

    ,

    n

    !

    {11

    uA3

    !,!

    41ei

    #")(

    $

    l

    n

    !,!

  • 8b ! A'!!

    1e,8W

    7Gh8 ^

    o

    8

    8W

    o

    @

    G8iihebWWhi8tbxiEGGEbWWZ8W

    WTeiebW

    n

    8

    n

    WW

    n

    @

    bi1W4eKih8GWW4i

    o

    8

    8W

    o

    @

    bG,WGT4W

    ;

    g

    n

    ;

    liK~ij8W

    n

    @

    ;= VGPnY

    `\eYP%XfeS

    y O^PY

    n

    o

    @9A,

    9

  • $ b! '!!

    e`ahX

    4

    2

    y^`ahX

    m

    y4OQP Y

    N-,

    %,

    C

    9

    8

    o

    @

    9

    N-,

    OQ\e~

    N-,

    C

    NLH

    iy

    `PZk8~xabc4SWp%ab[iXiS

    2

    EXiSWcQ|8VGSg

    I

    &

    WN-,

    N-,

    4

    SWXfe`PZk

    %IH

    NLH

    4

    d

    cb`\i[e~

    ~

    U

    N-,

    NLH

    U

    U

    %,

    N-,

    U

    .

    U

    N,

    NLH

    U

    .

    U

    NLH

    %IH

    U

    X4

    .

    U

    N-,

    NLH

    U

    SWXU`VG\

    TpL]Sx~

    6

    :

    Z!I

    :

    U

    N-,

    NLH

    U

    4

    OQP_GYnYahP%XiSWPZYP%X[et abPxX^]SW\iS8[i[iSW\RvYVGPGSm[VGabXiSmUZY\iXAakVTchavSW\iSwfSm_GY\iaYGcbSW[RYc]SxYXi`ah\iS8[RgcYr[iVTahXiSwfSW[

    n1`eS8PGPGS8[jY\iabXidGn]SWXia|WVTSW[jfGt VGPTSL[VGabXASmfSL_GY\iaYGcbSW[QabPZf]SWU9SWPZfTYP%XiSW[QSWXfSLn-eS8n1S=ch`ayOQPYSW[i`abP

    fGt VGPchSWnsn1SRg

    xOF Y

    %lbxG

  • 8b ! A'!!

    SWXkSWXiXiSRfSW\iPGavSW\iS|WV{YPxXiabX^]SXiSWPZf_SW\i[1Yi_S%k

    I

    y

    {{T0TWuOW

    7G

    "

    eT{eb

  • e

    &gf!)e GhiZbjhbk! #

    SkWYfe\iSr

  • 8b e

    &gf!)e hiZhGk! #

    1e,8W{

    7Gnm

    ;

    &p

    G1hbbjTRiKGeLee

    n

    hii

    m

    ;

    qp

    m

    ;

    WeeTRiKGee

    n

    uN'!6

    g ]S8_xafeS8PxXiSjS8XcYab[i[4]SSWPSWp%SW\ekakSxy

    z{Sxka4USW\in1S8XfGt ahP%Xi\i`^fVGab\iSjcY1f]SWTPGabXiah`P[iVGab_GYPxXiSg

    /

    %{Z85

    7G

    n

    9GshbbG^{ebW{G

    n

    rGlWbbiT

  • e

    &gf!)e GhiZbjhbk! #

    _E+`_ v 243%.EDG243

    /

    %{Z8{

    7T

    n

    m

    eWZW1Weieb

    NG,Wbh1Weiee

    n

    m

    G

    TZbh8b

    g

    m

    8hbj4e

    #"

    @&

    m

    "

    @

    ("

    +*

    ZI

    B[

    @

    "

    @,

    @

    #"

    @

    /

    x0!1324{

    s ^{ bWbN

  • 8b e

    &gf!)e hiZhGk! #

    TVU

    x1xu

    /

    %{Z8 WY

    GW%heTh4e1Weiee

    nS}

    EGG1WeiZ{ix{eZWbb

    ^

    cz

    #"

    }

    $

    l

    #"

    z

    $

    YRXidj]S8`\iahSfScYn1SW[iVT\iSYRU`VG\1GVTXwfeSfQ]SWGPTah\1VGPTSNahP%X^]SW\eYchS|8VGarfTYPG[1VGP;kSW\iXeYabPPG`nT\iS

    feSNkWY[UG\i`ch`PTSct abPxX ]^SW\eYchSfeS

    A

    ahS8nYPTPSWXEU`VG\EcY|WVTSWcbchSNfSW[E}`PZkXiab`PT[EUGcbVG[

  • e

    &gf!)e GhiZbjhbk! #

    TVU

    x1xu

    /

    %{Z8 F

    WTiWhGCG8G%hGs881W4biW"l%G,xi,WEZxx

    GG{W 8Gi8ebQGW{GxbT{1WeiebW{G

    n

    m

    GG

    le{hEGi1

    UDU

    URU

    8

    QWEZxx

    e

    G* T TlWbhW WZW!

    8

    4WTiWebjG8TxhTb^x%liebW

    h4x%lib80J2 BE@ID DG@IBEBFDG5 @ .EE2

    243%.EDG2

    TVU

    x1x5

    b^x%libjWeGi1hb8bieet

    8

    7G

    &

    8

    U

    U

    %

    U

    U

    &

    8

    X

    bbh%eii

    URU

    URU

    8

    U

    U

    %

    7G

    %

    %%{i

    d

    s

    7G

    x %

    ?

    bit

    ZiW^Q{eG

    Ey

    D

    yIj

    E^%{x5

    7GIGjGxbN1Weieb

    hi

    w

    ,

    yI

    7G

    gh

    8?

    W{W^b^

    G

    8

    yI

    yI

    yI,

    8

    yI

    y

    8WW"14ihWbGWbGWTWG8IGxh4x%lih8IGLbW1G%TGW#ll{bWIGxbT

    W^b^WebWLh4W3ibh8ij8#

  • 8b e

    &gf!)e hiZhGk! #

  • kh3!!)Z 5h! " b!

    vE+* N3%BE@I7^2+bE2?BEDGF,HE@IHEJ>AJ5LK23xZ@lDGJ@IHE>A243@I>9K24@I5%F,JDG243+

    `VG[NYcbch`PG[nYabPxXiSWP{YP%XY`\efeSW\cYmXidj]SW`\iahSfeS8[rUT\i`{YGabchabX^]SW[NfGYPG[XA`VTXASR[eYm

  • 8b kh3! ){!#h! "$ b!

    i

    #"

    @@!&

    m

    "

    ;

    ("

    +*

    x

    @!

    "

    @9l

    @u3

    #"

    @9

    /

    x0!1324{x~5

    T=^{ bZG lebWw eGl

  • kh3!!)Z 5h! " b!

    /

    %{Z8W

    7G

    m

    j

    euWZW1TEZieebbxW

    uGQ4e

    o

    gI

    We

    eGihebWbi^WWbhi{ b1l^WW Zi%4eTNT,h4W3ihbT

    Z

    o

    GZebW^

    #m

    E^%{

    7Z

    4bWGxbT84h4e8{ZL1i8Wei4{GWm

    `VG[LU`VG_`PG[YVG[i[af`PGPGS8\VGPGSfQ]S8GPGabXiah`P

  • 8b kh3! ){!#h! "$ b!

    /

    %{Z8 5

    wGl8hbrGxbwG^Zebwix88RbtiihebrWhi

    o

    ibxiTT

    4b1G%bp

    %MTGbQZ

    yt&

    '

    y{,

    o

    yI

    1e,8W{F

    7G

    o

    G1x{b1GWTix3^bi

    '

    yIl

    |

    SW[

  • kh3!!)Z 5h! " b!

    vE+ v F 24

  • 8b kh3! ){!#h! "$ b!

    I`VT\kS8cY~%`Pk8YckVTchS%~%U`VT\

    &;g

    U

    U

    .

    o

    U

    U

    o

    .

    U

    U

    o

    .

    x

    o

    n

    U

    o

    U

    .

    n

    U

    o

    U

    .

    x

    z{`n1n1SU`VG\LXi`VTX

    &=~

    U

    U

    .

    o

    ~%chSXi\iabP:e`n1SRfV[iSxk`P{fNfSW\^]SSWP

    ka

    fSW[i[iVT[

    PGSRk$dZYPGSUZY[fSj[ahPGS[iVT\;fe`PZk[i`Pfeab[ek\iabn1abPZYPxXS8[iXP]SWYXiah}i~%[i`abXg

    n

    U

    o

    U

    n

    U

    o

    U

    z{Sxka4UG\i`VT_SGabSWP|WVTSjcY1f]SWTPGabXiah`PUG\^]Sxk]SxfeSWP%XiSRYEVTPN[iS8PG[ey

    SjXidj]S8`\WvSWn1Sj[VGab_GYPxX}`VT\iPGabXVGPGSkWY\eYkX^]SW\iab[eYXiah`PfeScYEcb`aQg

    TVU

    x1x5

    7T

    o

    g

    G)iibebwWbiw^WWbb

    7T3CeTwG%b

    liKjb^xNlihW4 b4xNlibREe

    bi4h8ii8ebGLeeKi48i4RW4eKihW4W

    wWe{b1G8GixjGb1h4G

    o

    8^b ^~ij8jG

    GT

    n

    o

    il

    {{T0TWF

    ZWxW11G Ghbbim811mGbLj8h4e=,jbi8TWiTm

  • kh3!!)Z 5h! " b!

    vE+`_ jbK2B2bE@l=7^2

    m

    NSW[XVGP SW[iUZYkSCfeSUG\i`ZYTahcbabX^]S8[Gp=]Sxy

    Y fQ]S8GPGabXiah`P fSct abPZfQ]S8USWPZfTYPZkSCfSCfeSWVTp

    ]SW_=]S8PGSWn1S8PxXi[ISW[iX{cY,n-eS8n1Sj|8VGSkS8chcbSfeVkWY[Lfeab[ek\iS8X~8[YVT}{|WVTSQct `PPTSjk`PT[iafxvSW\iS|8VGSfeSW[ISWPT[iSWnGcbSW[

    feSjcYEXi\iabGV

    m

    g

    /

    %{Z8{

    7Gh8^

    "

    %A$TTXm

    "

    x$i4{GLbGlWGT4

    k")(

    $

    ,

    #"

    i

    $

    OQPUSWVGXYVT[iaQf]SWT\ct abPZfQ]SWUSWP{fGYPZkSfeSfeSWVTp_GY\iaYGcbSW[Yc]SxYXi`ah\SW[g

    /

    %{Z8 6 X

    %e iibebWu8biW

    o

    x

    4RTWubGjlWTG^8mx

    ixhWsW ^4i4e8hQ4e=ibW4^bWQh4W3ibh8

    &

    bWwWTW1W4

    o

    &

    x

    &

    i^{bGjlWTG^

    E^%{

    7G

    y&L

    W

    WWiiei3Gb^eG

    y

    W

    y

    ;=

  • 8b kh3! ){!#h! "$ b!

    vE+`v 0F,:x24D1,24E7^2+bE243)x{@IDGJ@lH=>A243@I>9K24@l5xF,JDG23

    ]SWGPTah[[i`PG[feab_S8\i[X%USW[feSk`Px_SW\iSWP{kSfGt VGPGS[iVGabXiSRfSj_GY\iaYGcbSW[Yc]SxYXi`ab\iSW[L\^]SWS8chcbSW[ey

    o

    @@!f]SW[ahPTSf`PZk=VGPGSm[VGabXASwfSm_GY\iaYGcbSW[RYc]SxYXA`ab\iSW[j\^]SWS8chcbSW[jS8X

    o

    VGPTSYVTXA\iSm_GY\iaYGcbSw|WVGa

    `VGSW\YEchS\!e`chSfeSchabn1abXAS%y

    z{`Px_SW\iS8PZkS

    eVGUTU`[i`PG[|WVGS

    !I

    &

    n

    o

    @

    SWX

    n

    o

    /

    %{Z8{

    NT{4e

    o

    @@!

    8'W#lq8i

    o

    GG

    cbahn

    @

    n

    i

    o

    o

    @

    ,

    z{`Px_SW\iS8PZkS

    8

    eVGUTU`[i`PG[|WVGS

    I

    &

    n

    U

    o

    @

    U

    S8X

    n

    U

    o

    U

    /

    %{Z8{

    NT{4e

    o

    @@!

    8'W#lq8i

    o

    GG

    8

    cbahn

    @

    n

    U

    o

    o

    @

    U

    ,

    z{`Px_SW\iS8PZkSSWPUG\i`ZYGabcbahX^]S

    /

    %{Z8{

    o

    @@u3

    W8#ljWZiehbx8Wi

    o

    54

    2

    U

    o

    @J

    o

    U

    2

    4

    z{`Px_SW\iS8PZkSUG\iSW[|WVTSj[eVT\iS

    /

    %{Z8{

    o

    @@u3

    W8#lQZi8i4ejeiW18^Wi

    o

    E>

    o

    @

    >LC

    o

    >=

    ,

    z{`Px_SW\iS8PZkSSWPch`a

    /

    %{Z8{5

    o

    @@u3

    W8#ljWb[Wi

    o

    NW^b^jxijWjT

    TG

    chabn

    @3

    n

    o

    @9A,

    n

    o

    i

    OQPYEchS\ ]^SW[iVTchXeYX[iVTah_GYP%X|WVTa \^SWchabSkSW[feab_SW\i[iSW[LPG`Xiah`PT[g

  • kh3!!)Z 5h! " b!

    TVU

    x1xF

    N1bWLhE{hbWbT

    W'8#l8GW!

    W'W#lWTW!

    8

    W'W#lWTWW{ieebhxW#

    W'8#l8GWWZieebbxWE

    W8#lWGWWhR

    W'8#l8GWZiW^ji

    W'W#lWTWW{ieebhxW#

    uN'!6

    g

    ;

    \eYkSYEcYEUT\i`UG\ia]SWX^]S

    n

    U

    o

    U

    n

    U

    o

    U

    f]SWn1`P%XA\4]S8SRfTYPT[cbSjXidj]S8`\WvSWn1S

    y

    y

    ~%`PNU9SWVGX]Sxk\iah\iSg

    n

    U

    o

    @m

    o

    U

    n

    U

    o

    @m

    o

    U

    kSR|8VGa4UT\i`VT_SR|8VGSjcY1k`PTSW_x\iS8PZkSfGYPG[

    abn1UGcba|WVTSjcY1k`P%_S8\iS8PZkSfGYPG[

    8

    y

    I`VT\Nf]SWn1`P%Xi\iSW\N|WVTSRcYk`P%_SW\iSWPZkSfGYPG[

    8

    abn1UGcba|8VGSRcYk`Px_S8\iS8PZkSRS8PUG\i`ZYTahcbabX^]S%~^`PY

    SW[i`abPfTt VTPNcbSWn1n1Sg

    xO Y

    %lbxG

  • 8b kh3! ){!#h! "$ b!

    OQPUSWVGXYcb`\i[UT\i`VT_SW\ct abn1UGcbakWYXiah`P_`VTchVTSjSWP%Xi\iSjcbSW[feSWVTpk`Px_SW\iSWP{kSW[g

    e`ahX

    k`P%XAabP%VGSSWX`\iP]SWS[iVG\=y4e`ahX

    4

    2

    y

    thYUT\WvSW[EcbScbSWn1n1SUG\ ]^SxkSxfeS8PxXe~T`P[eYabX1|WVZt `PU9SWVGXEXi\i`VG_SW\

    2

    XiSWc|8VGSN

    U

    o

    U

    2

    4

    y{OP

    PG`XiS

    "

    \

    U

    o

    U

    Ay4OPY1f`PZk

    #"

    @

    \

    4

    A

    SWnY\e|8VG`PG[|WVTS

    SW[iXVTPGab}`\in]SWn1SWP%Xk`P%XAabP%VGS[iVG\cbSk`n1UZYkX

    B

    \

    ??y&

    UU

    y

    U

    OQPUSWVGXXi\i`VG_SW\mz

    2

    EXAS8c|8VGS

    y

    &

    B

    \

    U

    y

    U

    zt

    U

    yI

    ^

    U

    4

    ,VTah[|WVTSj`PYEcY1k`P%_SW\iSWPZkSjS8PNUG\i`{YTahcbabX^]SW[e~

    6

    : &XiSWcQ|8VGS

    !I

    :

    U

    o

    @m

    o

    U

    2

    z{

    4

    OQPUSWVGXYcb`\i[]Sxk\iah\iS

    U

    n

    o

    o

    @i

    U

    n

    U

    o

    o

    @

    U

    C

    n

    U

    o

    o

    @

    U

    R

    GF

    -,

    |

    F+J

    4#.+

    n

    U

    o

    o

    @

    U

    R

    K

    GF

    -,

    |

    F+J

    4k.

    n

    U

    o

    o

    @

    U

    GF

    -,

    |

    FNM

    4

    4

    .

    >;

    #"

    @

    \

    .

    >;

    U

    o

    @J

    o

    U

    2

    z{C

    4

    .

    >

    4

    ` v^V> f]SW[ahPGSVGPnY

    `\YP%XfeS

    y

    z{SWXiXASUG\i`UG\ia]SWX^]SSW[iXabn1n]SxfeaYXiSxy

    SjUTchVT[e~%`PYfen1S8XAXi\eYEcbSj\4]S8[iVGcbXeYX[VGab_GYPxXg

    TVU

    x1x 6

    7G

    o

    @@!

    WW#l+Wi

    o

    GT

    8

    hib8xbe?eTieEQee

    o

    @33

    G

    o

    @@!

    8hbj4e

    o

    @3

    8W#lQ{iW4ejeiW18 ^Wi

    o

  • kh3!!)Z 5h! " b!

    vE+` wF,JJbE243,DG@lbE3EF HEDG2434+

    OQP_GY?nYabP%XAS8PZYPxX [et ahP%X^]SW\iSW[[iSW\e~k`n1n1SfGYPG[ cbSkWY[feab[ek\iS8X~vY cY [iVTahXiSfeS8[ n1`eSWPGPTSW[

    Y\iabXidGn]S8XAa|8VGSW[ufTt VTPGS[iVTahXiSfS_GY\iaYGcbSW[abPZfQ]SWUSWP{fGYPxXiSW[SWXfSneSWn1Scb`ayEOQPCYSW[`ahPCfTt VTP

    chS8n1n1Sx~4YPZYch`VGSvY1kSWcbVGaQfVk8Y[feab[ek\iS8Xg

    x5 Y

    %lbxG

  • 8b kh3! ){!#h! "$ b!

    vE+` w2?5K24FD'2 2?7^2468>Jk J5%2

    SXAdj]SW`\WvSWn1Su|8VGaQ}iYabXct `

    SWXNfSukSUZY\eY\eYUTdGSSW[iX[eYPG[fe`VGXiScbSRUTchVT[ahn1U`\iXeYPxXfeSXi`VTXiSW[

    chS8[UT\i`ZYGabchabX ]^SW[ey

  • b j )e h#' )J%" A /i#

    E+*

  • 8b h)e h#' b)J"% Ab /i#

    o

    ?,

    o

    ,

    8

    o

    ?,

    8

    o

    ,

    gch[

    `VGS8PxXfahp}`ab[S8XchS8[\^]SW[VGcbXYXi[L[i`PxXcbSW[L[iVGab_GYPxXi[

    88

    W

    OQP_`ahX1fe`PZk|8VZt abcZYSWV

    }`ab[1jSWX

    }`ah[

    yGqq

    `a|WVTSWn1SWP%Xiqq~T`Pf`ahXESWPk`PZkchVT\iSN|WVTScY

    ch`aQfeV

    S8VNSW[XkSWcbcbSR|8VGaQYi_GYPxXeYSjcbSR~4vYE[eYi_`ab\

    y

    E+`_ v F(,2=E2?25-xZ@lDGJ@IE7^2?2 B=JADGJ:

  • b j )e h#' )J%" A /i#

    E+`v wF,JmEF,D! @l>2?2455K24F,D'2 2?7^24m>Jk J5x2+/BEBE>JA79@[email protected]%5x3

    `VG[\eYUTUSWcb`PG[aka~j[i`VT[VGPGS}`\in1SUGcbVG[VGXiabchab[eYTchS%~jcY;fQ]SWGPTahXiab`P fGt VGPGScb`aYG[`cbVGnsSWPxX

    SW[i[iS8PxXiabSWcbchSfeV kWYckVGcQfeS8[UT\i`{YGabchabX ]^SW[ey

    /

    %{Z856

    sT94Z eTmiibebL^WWbbee9bbTGi1b8W44848Ze

    6r?

    i

    |i

    o

    |

    l

    X

    \

    =

    y

    z{SWXiXASch`a4SW[X

    %

    &

    _`ah\vYEcYETPfVk$dZYUGabXi\iSxkS|WVTa^U9SW\in1SWXfeSct VTXAabcbah[SW\ey

    SXid]SW`\WvSWn1S;kSWPxXi\eYc

    cbahn1abXiS

    y

    y

    |8VGSPG`VG[Yi_`PG[fQ]SWn1`PxXi\^]S;fGYPT[uchS;kWYf\iS;feSW[u_GY\iaYGcbSW[

    Yc]SxY\i`ab\iSW[|8VGSWck`P{|WVTSW[e~Q[et]SWPG`PZkS/YVG[i[asfScYw}iYk`P[iVTah_GYP%XiSx~j|WVGajSW[XUTchVT[YfGYUGX^]SWSYV kWY[

    feSW[L_GY\iaYGcbSW[feab[ek\WvSWXiSW[S8Xfe`PZkYVkWYfe\iSfeScYE[XYXiab[iXia|8VGSg

    TVU

    x1x 5

    7GbW^

    o

    8

    WW

    o

    @

    I iibh8WbiWwhTl8GG4WTuW1b

  • 8b h)e h#' b)J"% Ab /i#

    E^%{566

    xG

  • l1@IHE>2+bE243v @I5xJ24DG243

    z{dZYUGabXA\S

    iehbx8ebW

    P

    ZWWIhTb

    y

    8QV{t S8[iX

    kS|WVTSjcYEUG\i`ZYGabcbahX^]Sybyhybybyhybybyhybybyhybybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybybyhybybyhybybyhybybyhybybyhybybyhybybyhyby

    y

    \i`{YGabchabX^]Sj[iVT\VGPSW[UZYkSjTPGayQyhybybyhybybyhybybyhybybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybybyhybybyhybybyhybybyhybybyhybybyhybybyhyby

    y

    Y\iaYGcbSW[Yc]SxYXi`ab\iSW[L[iVT\VGPSW[iU{YkSRfSjUG\i`{YTahcbabX^]SjGPTayQybyhybybyhybybyhybybyhybybyhybybyhybybybyhybybyhybybyhybybyhybybyhybybyhybybyhyby

    y

    `aQfGt VGPGS_GY\iaYTchSYc]S%YXi`ab\iSj[iVT\VGPSW[UZYkSRfSjUT\i`{YGabchabX^]SjTPGaymyhybybyhybybybyhybybyhybybyhybybyhybybyhybybyhybybyhyby

    y

    [iU]S8\eYP{kSjS8X_GY\iaYPZkSRfTt VTPGSj_4ybYEGPGabSxyybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybybyhybybyhybybyhybybyhybybyhybybyhybybyhyby

    y

    gPZfQ]S8USWPZfTYPZkS[iVG\LVGPSW[iUZYkSRfeSUG\i`ZYTahcbabX^]SGPTayIybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybybyhybybyhybybyhybybyhybybyhybybyhybybyhyby

    z{dZYUGabXA\S

    iehbx8

    X

    biW%xW

    y

    [iUZYkSfeSUG\i`ZYGabcbahX^]SW[f]S8PG`nG\eYGcbSxy1ybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybybyhybybyhybybyhybybyhybybyhybybyhybyby

    y

    Y\iaYGcbSW[Yc]SxYXi`ab\iSW[feab[ek\WvSWXiSW[Nybybyhybybyhybybyhybybyhybybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybybyhybybyhybybyhybybyhybybyhybybyhybyby

    y

    [iU]S8\eYP{kSRfTt VTPGS_ y^bYyhfah[k\WvSWXiSxy1ybyhybybyhybybyhybybyhybybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybybyhybybyhybybyhybybyhybybyhybybyhybyby

    y

    gPZfQ]S8USWPZfTYPZkS[iVG\LVGPSW[iUZYkSRfeSUG\i`ZYTahcbabX^]Sfeab[ek\iS8Xyybyhybybyhybybyhybybyhybybyhybybyhybybyhybybybyhybybyhybybyhybybyhybybyhybybyhybyby

    y

    pxSWn1UTchS8[abn1U`\iXeYP%Xi[fSjcb`ah[feab[ek\8vS8XAS8[sybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybyhybybybyhybybyhybybyhybybyhybybyhybybyhybyby

    y

    `P{kXiah`PT[

  • jb=2 bE23-bK2=EJ5%JF,E3

    kWY\eYkX^]SW\iab[eYXAab`PfeSEcYLcb`a,fGt VGPGS_4yhYy\^]SWS8chcbS

    k`PxXiabPxVTahX ]^SfGt VGPGSn1SW[iVT\iSyyyTyyyTyyyyTyy

    k`Px_SW\iSWP{kSfGYPG[

    8

    yyTyyyTyyyTyyyyTyy

    k`Px_SW\iSWP{kSfGYPG[

    yyTyyyTyyyTyyyyTyy

    k`Px_SW\iSWP{kSSWPNcb`a yTyyyTyyyTyyyTyyyyTyy

    k`Px_SW\iSWP{kSS8P cb`afTt VTPGS [iVGabXiSfeS _^yYy

    feab[ek\WvS8XAS8[ yTyyyTyyyyTyyyTyyyTyyyTyyyyTyy

    k`Px_SW\iSWP{kSSWPNUT\i`ZYGabchabX^]S yTyyyTyyyyTyy

    k`Px_SW\iSWP{kSESWPUG\i`ZYGabcbahX^]S1fGt VGPGSE[iVGabXiSmfS=_4y

    Yy4fah[k\WvSWXiSW[ yyTyyyyTyyyTyyyTyyyTyyyyTyy

    k`Px_SW\iSWP{kSUG\iSW[|WVGS[eVT\iS yyTyyyTyyyyTyy

    feSWPT[iabX^]SfGt VGPTSj_4yhYy%\^]SWS8chcbSyyyTyyyTyyyyTyy

    SW[iU{YkS

    8

    yyyTyyyyTyyyTyyyTyyyTyyyyTyy

    SW[iU{YkSRfeSUG\i`ZYTahcbabX ]^S yyTyyyTyyyTyyyyTyy

    SW[iU{YkSRfeSUG\i`ZYTahcbabX ]^Sf]S8PG`nG\eYGcbS yTyy

    SW[iUj]SW\eYPZkSfGt VGP_^ybYy%GPGabS yyTyyyTyyyyTyy

    SW[iUj]SW\eYPZkSfGt VGPGS_4yhYy4feab[ek\WvSWXiS yyTyyyyTyy

    SW[iUj]SW\eYPZkSfGt VGPGS_4yhYy \ ]^SWSWcbcbSRvY1feS8PG[iabX ]^S yTyy

    }`PZkXiab`P feSu\ ]^SWUZY\iXiabXAab`P fGt VGPTS_4ybYyfeab[ek\WvSWXiS

    }`PZkXiab`PfSj\^]SWU{Y\iXAabXiah`PfGt VGPTSj_4yhYy%\ ]^SWS8chcbS

    }`PZkXiab`PN