http://www.Beiki.info o o o o o o o

http://www.Beiki.info o o o o o o o

http://www.Beiki.info o o o o o o o

o o o o 2 http://www.Beiki.info o tX u ( X ) e t 2Y u ( X , Y ) et1 X t n Z u ( X , Y ,..., Z ) et1 X t 2Y ... 3 http://www.Beiki.info

o : X )MX(t etX )MX(t)=E(etX |t<=|c . c ) MX(t tx )(t ) X f ( x : X : 4 e (t ) e f ( x)dx tx http://www.Beiki.info X M M o : X )MX(t etX )MX(t)=E(etX |t<=|c . c ) MX(t tx )(t ) X f ( x : X : 5 e (t ) e f ( x)dx tx

http://www.Beiki.info X M M 2 tx e 3 ( tx ) ( tx ) 1 tx ... 2! 3! 2 tx o tx E (e ) x e f ( x) x 3 ( tx

) ( tx ) [1 tx 2! 2 3! ...] f ( x) 3 x f ( x) t x xf ( x) t x x f ( x) t x x f ( x) ... 2! 3! 2 2 3 3 r 1 t t t ... t ... 1 2! 2 3! 3 r! r http://www.Beiki.info 6 o d MX(t) : E ( X ) M (t ) ] r :2 dt 3

r : M X (t ) 1 t 1 t2! 2 t3! 3 ... tr! r ... r r r X 2 2t (1) ( t ) M X 1 2! 2 33t! t 0 r r 1 ... rtr! ... M 3 r (1) X (0) 1 r 2 M ( 2) M (r ) X

X ( r 1 ) t 2t (t ) ... 2 2! 3 (r 1)! ... M r ( 2) X (0) 2 (t ) ; r 1,2,3,... r http://www.Beiki.info 7 o X : 39 x n x n f ( x) C x p (1 p) ; x 0,1,2,3,..., n

n p<=1=<0 X . 8 http://www.Beiki.info o x n x n tx tx n : M X (t ) E (e ) x0 e C x p (1 p) n t n x 0 C x ( p e ) M (1) X t x n x (1 p) t (t ) np e [ p e t ( 2) t

[ p e n 1 p] n 1 1 p] n 2 t t M (t ) np e (1 p np e )[ p e 1 p] M (0) np; M (0) np(1 np(1 p) X (1) ( 2) X 2 p np) 2 2 X X 1 2 http://www.Beiki.info 9 o

:43 X x ; x 0,1,2,3,... !x . tx X tx e !M X (t ) E (e ) x0 e x : x t ) ( e t t e x 0 ])e Exp( e ) Exp[ (e 1 !x http://www.Beiki.info 10 x e f ( x) o : X Y ) MX(t ) MY(t t ) MX(t)=MY(t X Y . 11

http://www.Beiki.info o :46 1 : ) (t X; t 1 X M 1 t 1 tx ; e f ( x)dx t 1 1 t x f ( x) e ;0 x 1 ( t ) ;t 1 M 1 t X X x f ( x) e ;0 x 12 http://www.Beiki.info

o : ... X1 X2 Xn (t ), M (t ),..., M (t ), M X X X Y=X1+X2++Xn Y n ) (t 13 Xn (t ) * ... * M 2 2 1 M Y (t )M X (t ) * M X 1 http://www.Beiki.info o :47 X Y x y f ( x, y ) ;0 x ,0 y e

Z Z=X+Y Z 14 http://www.Beiki.info o : x y x y x y g ( x) e dy e ;0 x , h( y ) e dx e ;0 y 0 M 0 X tx (t ) e 0 e x ty y 1 1 dx ; t 1, M Y (t ) e e dy ;t 1 0 1 t 1 t 2 1

M (t ) M (t )*M (t ) ( ) ; t 1 1 t Z X Y http://www.Beiki.info 15 o : ) f(x,y ( E ) M Y (t1 ,X et X t Y )t 2 X ,Y X Y . : M X ,Y (0, t 2) M Y (t 2), M X ,Y (t1 ,0) M X (t1), M X ,Y (0,0) 1 2 1 k m ) m Y k ) ( , E ( X X ,Y t1 t 2 ] 0 , 0 t1 t 2 M t t m

k 2 1 2 ] )(t1 , t 2 t10,t 20 16 X ,Y M t t 2 k1,m1 E ( XY ) 1 http://www.Beiki.info o Y X : M X ,Y (t1 , t 2) M X (t1) * M Y (t 2) f ( x, y ) g ( x ) * h( y ) t1 X t 2Y ) t1x t 2 y f ( x, y )dxdy ( , ) E ( M X ,Y t1 t 2 e e e: X Y x y

et1 g ( x)dx et 2 h( y )dy M X (t1) M Y (t 2) X y t1 X t 2Y ) E ( t1 X ) E ( t 2Y ) ( , ) ( ) ( ) E ( e e e e M X ,Y t1 t 2 M X t1 M Y t 2 t1xt 2 y f ( x, y )dxdy t1x g ( x)dx t 2 y h( y )dy t1xt 2 y g ( x)h( y )dxdy e e e e X Y X y X Y f ( x, y ) g ( x ) h ( y ) http://www.Beiki.info 17 o : X ) f(x :

Xx X )(t ) E (t ) x t f ( x X ||t d . (1) k 0 xf )( x E ( X ) <=1 X dt : 18 http://www.Beiki.info o :48 X X

x (t ) E (t ) x t f ( x) d (1) k 0 xf ( x) E ( X ) X dt http://www.Beiki.info 19 o :48 X x n x n f ( x) C x p (1 p) ; x 0,1,2,3,..., n n p<=1=<0 x x n x nX x n )(1 p X (t ) E (t ) x0 t C x p . x n x n n n : ] x 0 C x ( pt ) (1 p) [ pt 1 p )(1 , X (1) np 1 20 n 1

]p (t ) np[ pt 1 http://www.Beiki.info )(1 X o :1 a b X : E(aX+b)=aE(X)+b : E (aX b) (ax b) f ( x)dx a xf ( x)dx b f ( x)dx aE ( X ) b E(b)=b :1 E(aX)=aE(X) :2 21 http://www.Beiki.info o :2 /

X / : E ( g ( X ) h( X )) ( g ( x) h( x)) f ( x)dx : ]) g ( x) f ( x)dx h( x) f ( x)dx E[ g ( X )] E[h( X 22 http://www.Beiki.info o :2 / X Y / : E[u ( X , Y ) v( X , Y )] [u ( x, y ) v( x, y )] f ( x, y )dxdy : u ( x, y ) f ( x, y )dxdy v( x, y ) f ( x, y )dxdy ]) E[u ( X , Y )] E[v( X , Y ]) E[ g ( X ) h(Y )] E[ g ( X )] E[h(Y :1 :2 23 ) E[ X Y ] E ( X ) E (Y http://www.Beiki.info

o Y X :4 : E(XY)=E(x)*E(Y) f ( x , y ) g ( x ) h ( y ) E ( XY ) xyf ( x, y )dxdy : E ( XY ) xyg ( x)h( y )dxdy xg ( x)dx yh( y )dy E ( X ) * E (Y ) http://www.Beiki.info 24 2 aX b 2 aX b o

X b a :1 2 2 2 2 : aX b Var (aX b) a Var ( X ) a X E{[(aX b) 2 aX b] }, a b : E (aX b a b) a E ( X ) a 2 X X aX b 2 X 2 2 2 X 2 2 a :1 2 X b aX 2 X 2 X

:2 http://www.Beiki.info 25 Y X :2 f(x,y) 2 2 2 2 aX bY Var (aX bY ) a Var ( X ) b Var (Y ) 2abCov( X , Y ) a 2 aX bY E{[(aX bY ) 2 b2 2 X Y 2ab XY aX bY ] }, a b : E{[(aX bY ) (a X b Y )] } E{[(aX a X ) (bY b Y )] } a E[( X ) ] b E[(Y ) ] 2abE[( X )(Y )] a 2 b2 2ab X Y 2 aX bY X Y 2 2

o 2 aX b 2 2 2 2 X 2 aX bY a 2 X b2 2 Y 2 2 X Y XY 2 Y Y X :1 2 Xn2 ...2 2 X2 X21 :2 2 2 aX 1 1

a2 X 2 ...an X n a1 X1 a 2 http://www.Beiki.info X2 ... a n Xn 26 o :3 X Y 1 1 1 . XY 2(1 ) : 1 XY 1 27 XY XY ) XY ) 2Cov( X , Y Y

2(1 X Y ) 2X Y2 X ) 2Cov( X , Y Y 2 2 X ( 0 Var X Y ( 0 Var ) Y X 2 2 Y 2

X 2 Y X Y Y X X http://www.Beiki.info o Cov(X,Y)=Cov(Y,X):1 Cov(X,X)=Var(X) :2 Cov(a1+c1X,a2+c2Y)=c1c2Cov(X,Y) :3 Cov (a1 c1 X , a2 c2 Y ) E[(a1 c1 X [c1 E ( X : a c )(a c Y a c 1 1 X 2 2 2 2 Y )]

) c E (Y )] c c Cov( X , Y ) X 2 Y 1 2 http://www.Beiki.info 28 o Z Y X :4 fX,Y,Z(x,y,z) Cov(X,Y+Z)=Cov(X,Y)+Cov(X,Z) Cov( X , Y Z ) E[ X (Y Z )] E ( X ) E (Y Z: ) E ( XY ) E ( XZ ) E ( X ) E (Y ) E ( X ) E ( Z ) [ E ( XY ) E ( X ) E (Y )] [ E ( XZ ) E ( X ) E ( Z )] Cov( X , Y ) Cov( X , Z ) http://www.Beiki.info 29 m o n Y X :5 ... X1 Xm2 n

n m Cov(i 1 X i, : ) Cov( X ) Y1 Y2 Xn Ymi,Y ... j j j 1Y i 1 j 1 j 1 j i 1 i n n : m m E ( X i ) , E (Y j ) j E (i 1 X i ) i 1 , E ( j 1Y j ) j 1 j i i n m n n Cov(i 1 X i, j 1Y j ) E[(i 1 X i m

m )( Y )] E[ ( X ) (Y )] E[ ( X )(Y )] E[( X )(Y )] Cov( X ,Y ) n i 1 m i i 1 n m i 1 j 1 i i j 1 i j j j j http://www.Beiki.info n m i 1 j 1 n

m i 1 j 1 j j 1 i i j 1 j i i j j j 30 n n n n m o : | X j Y j Var (i 1 X i ) Cov(i 1 X i, j 1 X j ) i 1 j 1 Cov( X i , X j ) , ) 2 i j Cov ( , )

i j Cov ( m j 1Var ( X i ) i j Cov( X i , X j ) Xi Xj X iXj n m Var (i 1 X i ) j 1Var ( X i ) 2i j Cov( X i , X j ) : Xj Xi n m Var (i 1 X i ) j 1Var ( X i ) http://www.Beiki.info 31 o :59 ... X1 X2 Xn 2 n 1 X i 1 X i n S2 2 n S 2

) i 1 ( X i X 2 S 2 ] S n 1 [Var ( X ), E n 1 32 . http://www.Beiki.info 2 1 1 1 n n Var ( X ) Var ( i 1 X i ) ( ) Var (i 1 X i ) ( ) n .: 2 n Var ( X i ) n 2

2 n 2 n n n S ( X i X ) [( X i ) ( X )] ( X i ) ( X ) 2( X ) ( X ) ( X i ) n ( X ) 2( X )n( X ) ( X i ) n ( X ) E ( S ) E[( X i ) ] n ( X ) n nVar ( X ) (n 1) E ( S ) 2 n 2 i 1 2 n i 1 2 n n i 1 i 1 2 2 n i n

i 1 2 2 i 1 2 2 n 2 i 1 2 n i 1 o i 1 2 2 2 2 n 1 http://www.Beiki.info 33 o :1 X a ) t ( X a at

tX at atM ( t ) E ( ) E ( ) M (t)=e )(t X+a e ) e eX e M X (t M X a : :2 X a ) t ( aX ( at ) X ( t ) E ( ) E ( e e ) M X (at ) : M aX )MaX (t)=MX(at : 34 http://www.Beiki.info o

:3 ... X1 X2 Xn (t ), i 1,2,..., n M X n i 1 a i Xi Y n ( t ) ) (ai t X: M Y i1 M i i tY ) t ( a1 X 1 a2 X 2 ..an X n t ( a1 X 1 t a2 X 2 t an X n ( t ) E ( ) E ( ) E ( ... e e e e : )e MY ta X i i ) M ( ai t a1 X 1) E ( a2 X 2)...E ( an X n) e )

X i e e ) ( ai t 35 n Xi (an t ) i 1 M Xn (E t t (a2 t )... M (a1 t ) M X2 X1 (t E (e M Y (t ) M http://www.Beiki.info o :1 . :2 X Y X ) t( (t ) * Y ) t( Z=X+YZ

Y : )t X ) E (t X Y Z (t ) E (t ) E (t Y Z X ) E (t ) E (t ) X (t ) * Y (t 36 http://www.Beiki.info o RY [ ]X,Y Y=y | E ( X y ) x f Y=y ( x | y X ) X |Y X |Y R 2. 2

) Var ( X | y ) X |Y ( x X |Y ) f ( x | y X |Y R y y o ( x | y )dx ( x | y )dx 37 X |Y f 2 X |Y f x Ry X |Y E ( X | y ) ) Var ( X | y ) X |Y ( x X |Y Ry http://www.Beiki.info 2 o Var ( X | Y y ) E ( X 2 | Y y ) [ E ( X | Y y )]2 E (u ( X | y ) u ( x) f X |Y ( x | y )dx RY n n

] E (i 1 X i | Y y ) i 1 E[ X i | Y y 38 http://www.Beiki.info :65 E(X|Y=y) . y Y X e e f ( x, y ) ;0 x ,0 y . x x y y y x h( y ) ( y )e e dx e [ e y ]0 e y 1 y y 0 x y y x ( ) e e f ( x, y ) y y 1 f X |Y ( x | y )

( ) e y y h( y ) e 1 o x x o x E ( X | Y y ) ( )e dx [ xe ye y ]0 0 y lim x xe x y x y y y y http://www.Beiki.info 39 o

: X Y ) Y(X|Y)[=E(X . ) y E ( X | Y y)h( y) E ( X ) E ( X | Y y)h( y)dy E ( X : |EY]EX ) E ( X | Y y )h( y ) y [ x xf ( X x | Y y )]h( y ) f ( X x, Y y ) ]h( y ) x x y f ( X x, Y y ) h( y y [ x x ) xg ( x) E ( X 40 y http://www.Beiki.info x o :68 3 3 5 7 . . )E ( X ) y E ( X | Y y )h( y ) E ( X | Y 1) P (Y 1) E ( X | Y 2) P(Y 2) E ( X | Y 3) P(Y 3 : X Y 1 ) [ E ( X | Y 1) E ( X | Y 2) E ( X | Y 3)]; E ( X | Y 1) 3; E ( X | Y 2) 5 E ( X 3 1

; E ( X | Y 3) 7 E ( X ) E ( X ) [3 5 E ( X ) 7 E ( X )] E ( X ) 15 3 41 http://www.Beiki.info o Y X : : Var ( X | Y ) E ( X 2 | Y ) [ E ( X | Y )]2 Y )]E ( X ) E[Var ( X Var(E(X|Y)[+E(Var(X|Y)[=Var(X) | Y )] E[ E ( X 2 | Y )] E{[ E ( X | Y )]2 } E[ E (X | 2 2 : E[Var ( X | Y )] E ( X ) E{[ E ( X | Y )] } 2 2 )]E ( X ) Var [ E ( X | Y )] E{[ E ( X | Y )]2 } {E[ E ( X | Y )]}2 E[ E (X |Y Var [ E ( X | Y )] E{[ E ( X | Y )]2 } [ E ( X )]2 E[Var ( X | Y )] Var [ E ( X | Y )] E ( X 2 ) [ E ( X )]2 Var ( X ) http://www.Beiki.info 42 o :70 ... X1 X2 N N ) Var (i 1 X i N N E[i 1 X i | N .

] NE ( X );Var (X ) [i 1 X i | N ] NVar N N N : ]) Var ( X i ) E[Var ( X i | N )] Var [ E ( X i |N i 1 i 1 i 1 ]) E ( NVar ( X )] Var [ NE ( X 43 ) E ( N )Var ( X ) [ E ( X )]2 Var ( N http://www.Beiki.info o F F X=1 F X=0 )E(X)=P(F Y ) P( F ) E ( X ) y P( F | Y y )h( y E(X|Y=y)=P(F|Y=y);P(F)=E(X)=E [)Y]EX|Y(X|Y P( F ) E ( X ) P( F | Y y )h( y )dy 44 http://www.Beiki.info

o Y X :73 h(y) g(x) . Z=X+Y FZ ( z ) P ( X Y z ) P( X Y z | Y y )h( y )dy: P( X z y )h( y )dy G X ( z y )h( y )dy d d f Z ( z ) FZ ( z ) G X ( z y )h( y )dy dz dz d dz GX ( z y)h( y)dy g X ( z y)h( y)dy http://www.Beiki.info 45 o :74 X Y f X ( x) fY ( y ) 1;0 x 1,0 y 1 Z=X+Y . 1 f X Y ( z ) g X ( z y )(1)dy : 0 0 y 1 1 y 0 z 1 z y z z 0 z 1 f Z ( z ) (1)(1)dy z 0

1 46 1 z 2 f Z ( z ) (1)(1)dy 2 z z 1 http://www.Beiki.info o Y X : : X g(X) E{]Y-g(X)[2<=E{](Y-E(Y|X)[2} E{[Y g ( X )]2 | X } E{[Y E (Y | X ) E (Y | X ) g ( X )]2 | X } : E{[Y E (Y | X )]2 | X } E{[ E (Y | X ) g ( X )]2 | X } 2 E{[Y E (Y | X )][E (Y | X ) g ( X )] | X } E{[Y E (Y | X )][E (Y | X ) g ( X )] | X } [ E (Y | X ) g ( X )]E{[Y E (Y | X )] | X } [ E (Y | X ) g ( X )][E (Y | X ) E (Y | X )] 0 E{[Y g ( X )]2 | X } E{[Y E (Y | X )]2 | X } E{[ E (Y | X ) g ( X )]2 | X } 2 g ( X )] | X }0 E{[ E(Y | X) E{[Y g ( X )]2 } E{[Y E (Y | X )]2 } http://www.Beiki.info 47 o :75 X Y )E(Y|X . a b Y X : a X g(X)=a+bX , b Y X X :

Y X a b 2 2 ]) E{[Y (a bX } E[Y 2 2aY 2bXY [) a 2 2abXE{]Y-(a+bX }( b 2 X 2 ]; E (Y 2 ) 2aE2 Y ) 2bE ( XY ) a ) 2abE( X ) b 2 E ( X 2 2 ) E{[Y (a bX )]2 } 2 Y 2a 2b X 0; E{[Y (a bX )]2 } 2 E ( XY 2a X 2bE ( X ) 0 a b Y X , b Y X X 48 http://www.Beiki.info a Y

Related Presentations

Arena Blended Connected (ABC) learning design workshop
Arena Blended Connected (ABC) learning design work...
The GreenPlan First Presentation - Alison
The GreenPlan First Presentation - Alison
Statoakustický aparát - Univerzita Karlova
Statoakustický aparát - Univerzita Karlova
Extra Course Day 1 - Noji
Extra Course Day 1 - Noji
UNIT 6: Chemical Equilibrium
UNIT 6: Chemical Equilibrium
The Air We Breath - Metropolitan Community College
The Air We Breath - Metropolitan Community College
Common Core State Standards - RPDP
Common Core State Standards - RPDP
Trace Evidence - sites.google.com
Trace Evidence - sites.google.com

Recently Viewed Presentations

  • The Hunger Games

    The Hunger Games

    The Hunger Games. 1. What is the meaning of the title? 2. What do you make of the beginning of the novel? 3. What are the meanings of the names? 4. What symbolic objects have you noticed? 5. What allusions...
  • 360 Degree Panoramic Photography

    360 Degree Panoramic Photography

    Title: 360 Degree Panoramic Photography Author: karl.harrison Last modified by: karl.harrison Created Date: 1/30/2006 12:17:26 PM Document presentation format
  • Diapositive 1 - Martine Mottet

    Diapositive 1 - Martine Mottet

    Carine Paquin Cynthia Pelletier Virginie Tremblay Plan de la communication 1. Description générale du type d'activité 2. Description détaillée du déroulement 3. Ressources requises 4. Conseils à l'enseignant 5. Liste d'exemples de mise en œuvre 6. Conclusion 7.
  • Chapter 8

    Chapter 8

    A Recognition Task Which of the following are names of the Seven Dwarfs? Goofy Bashful Sleepy Meanie Smarty Doc Scaredy Happy Dopey Angry Grumpy Sneezy Wheezy Crazy Spreading Activation Model Activation Level: The internal state of a memory, reflecting its...
  • Aurora - 12P GS140 700 MHz vs. 16P Gs1280 1.15 GHz

    Aurora - 12P GS140 700 MHz vs. 16P Gs1280 1.15 GHz

    OpenVMS "Marvel" EV7 Proof Points of Olympic Proportions Tech Update - Sept 2003 [email protected] OpenVMS Marvel EV7 Proof Points of Olympic Proportions Live, mission-critical, production systems Multi-dimensional Before and after comparisons Upgrades from GS140 & GS160 to GS1280 Proof of...
  • Objective: To develop a tool box of passes

    Objective: To develop a tool box of passes

    Goal 1/3 of the netball court Equipment: 1 ball per pair Pairs stand facing each other in a line. Do 10 each way of the following passes Chest (arms by side, hands make a W with thumb tips touching, ball...
  • 5.1 living places - Weebly

    5.1 living places - Weebly

    community- the living part, (all the different organisms living in that particular habitat) ... MRS GREN TASKs Watch the life process video and answer the questions on your worksheet . Cut and Paste Activity - Match up the life processes...
  • ISR Testing Playbook - Workday@Yale

    ISR Testing Playbook - [email protected]

    [email protected] Release 4 Impacted System Remediation (ISR) Forum:System Integration Testing. December 5, 2016. Terminology. Test Schedule. ISR Integration Testing Process. ISR Checklist. ISR Integration Testing Calendar. ... Report the defect status on a daily basis to Test Lead.