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(2 AE   Z!  fԔL!?"6@ NNN?N% o,$ 0 p(I)T 2EEEE ! Z!  fԔL!?"6@ NNN?N ,$  0 p(J)T 2EEEE' & # ll!  fԔL!?"6@ NNN?ND od  MStates of the world 2E(F   '   ( T3ԔX)?"6@ NNN?N  ) ZL#!  fԔL!?"6@ NNN?N-M 8 = {1,2,3,& ,n}(2e33ee33ee33ee33ae33e$B * TDjJL!?"0@NNN?N  ,$D  0: ,@ c 0e0e    B9C@DE(F   jJ L!     ?A)BCD|E|| [Q$GJ9@ @   # "0e@       @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab m!g,$D  0 - Z.!  fԔL!?"6@ NNN?N] },$ 0 p(I + J)x 2EEEEEE9 . Z7!  fԔL!?"6@ NNN?N 8,$ 0 =.  2G6H  0޽h ? ̙33GG___PPT10F.H P6@+׎ D"D' N! = @B DC' = @BA?%,( < +O%,( < +D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bwipe(up)*<3<* DG' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(Dh' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D' =%(D' =%(D)' =4@BB BB%(D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(Dw' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(Dh' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(Dh' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*!%(D' =-g6B fade*<3<*!D' =%(D' =%(D)' =4@BB BB%(D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(D_' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D]' =%(D' =%(D' =A@BBBB0B@?%(D' =1:Bvisible*o3>+B#style.visibility<*%(D]' =%(D' =%(D' =A@BBBB0B@?%(D' =1:Bvisible*o3>+B#style.visibility<*%(D]' =%(D' =%(D' =A@BBBB0B@?%(D' =1:Bvisible*o3>+B#style.visibility<*%(D]' =%(D' =%(D' =A@BBBB0B@?%(D' =1:Bvisible*o3>+B#style.visibility<*%(D]' =%(D' =%(D' =A@BBBB0B@?%(D' =1:Bvisible*o3>+B#style.visibility<* %(D]' =%(D' =%(D' =A@BBBB0B@?%(D' =1:Bvisible*o3>+B#style.visibility<* %(D]' =%(D' =%(D' =A@BBBB0B@?%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =%(D' =%(Dg' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<**%(D' =-s6Bwipe(down)*<3<**Ds' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-o6Bwipe(up)*<3<*,D' =%(Dh' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*.%(D' =-g6B fade*<3<*.D' =%(Dh' =A@BB BB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*-%(D' =-g6B fade*<3<*-++0+0 ++0+ 0 ++0+ 0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+ 0 ++0+!0 ++0+-0 ++0+.0 +  0L0   !/ (    c $t1|   GThe combination axiom< ! c $8?f> s9p?"6?@`NNN?NF `XP___PPT92* For every I, J I, p(I + J) [p(I), p(J)]. If p(I) p(J), then p(I + J) (p(I), p(J))*c "  g$c$g$c$g$c$$c$$c$cg$c$g$c$g$c$$c$c(g$c$g$c$g$c$g$c$c(c$cc$g$c$g$c$g$c$$c$g$c$g$c$g$g$gc$g$c$g$c$g$c$$c$c(g$c$g$c$g$c$g$c$c(     0bcH  0޽h ? ̙33___PPT10i.H P6@+D=' = @B +3 0L0  }(  v l   ,$D  0   `e! fԔ L!? `:(ii) For each case j, there exists a probability vector pj in (), not all of them on the same line, and positive weight sj , such that for each memory I rGGGG$GGOGCG33C7cgfofkcgG`89!  0   Z~!  fԔL!?"6@ NNN?N vd * Sj d" m I(j) sj pj p(I) = _________________ Sj d" m I(j) sj_0P2GCGCGGfOfGGOGGGCGCK&CGCGCGfOft2  6!  <,$ 0 BThe main theoremb  Z!  fԔL!?"6@ NNN?N,$ 0 f,The following two statements are equivalent:- 2-E   `! fԔ L!?n,$D  0 Tp(i) The probability formation function p satisfies the combination axiom, and its range does not lie on a line. qGGGGGGIG  0pqW   `̮! G>>HԔL!?"6@ NNN?N ,$D 0 UiThe probabilities pj are uniquely determined, the weights sj - up to multiplication by the same scalar.j(2EGO(Egfof,E,(,2    ` ԔL!?"6@ NNN?N ,$D  0H  0޽h ? ̙33!|!___PPT10\!. Č+UE D ' ! = @B D' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =%(D@' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-o6Bwipe(up)*<3<* D ' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<* D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<* D' =%(DV' =A@BB5BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*DK ' =%(D' =%(DP' =A@BB5BB0B%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*D' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*D' =-g6B fade*<3<*D' =1:Bhidden*o3>+B#style.visibility<*%(DC' =4@BB5BB%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<* D' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<* D' =-g6B fade*<3<* D' =1:Bhidden*o3>+B#style.visibility<* %(++0+0 ++0+0 ++0+0 ++0+0 ++0+0 + : 0L0  H(     `!  fԔL!?"6@ NNN?N vd * Sj d" m I(j) sj pj p(I) = _________________ Sj d" m I(j) sj_0P2GCGCGGfOfGGOGGGCGCK&CGCGCGfOft2 l    .j ,$D  0   f3o s9p?"0@NNN?N @  7  ]     f! oL!?"0@NNN?N4 7 MDenote by the vector of frequencies of cases in I. BN JEEE@    J \    f! oL!?"0@NNN?N [ =I (2E  C x$ oL!?"0@NNN?NoT  Sj d" m I(j) (2OfGCGC  # l$ oL!?"0@NNN?NYD @________ (2 AK   f@ $ oL!?"0@NNN?N  uFI = T(2EMAE   fx$ oL!?"0@NNN?N # ,$ 0 tDividing nominator and denominator by Sj d" m I(j), yiealds; 2&EMfEAE A,-  6$  ,$ 0 T"The probability formation function##v  T $  3ԔL!?"6@ NNN?N U,$D 0  Sj d" m FI(j) sj pj p(I) = _________________ Sj d" m FI(j) sj "d0P2GOCGCGGfOfGGOGGGCGCK&CGOCGCGfOfCCt1H  # l8C$ G̈HoL!?"0@NNN?Nq,$D 0 @XSince p(I) depends on FI only, we can write& -(2EEAEA EEME$  # lM$  oL!?"6@`NNN?Nb V,$D  0 p(FI)b(2EAEMAH  0޽h ? ̙33___PPT10. Č+D' \$ = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D8' =A@BB@BB0B%()?)?D' =.G7 BBBBBYM 1.11111E-6 4.44444E-6 L 0.00156 -0.59121 *3>*B ppt_xB ppt_y=@0BBAApBBa 6:B Y<*D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D' =%(Dc' =4@BBBB%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-o6Bwipe(up)*<3<*D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(DR' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-6B%slide(fromBottom)*<3<*D*' =%(D' =%(Dz' =A@BB5BB0B%(E' =1B B`BPB1:Bhidden*3>+B#style.visibility= `B<*D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =-g6B fade*<3<*D' =%(DS' =%(D' =A@BBBB0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*+P+0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 +- 0L0 Db5,$D)  0B  @  `D3jJL!?"0@NNN?N A7,$D-  0   0e0e    BTCDEF̙R o L!     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||T @` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab= s4,$D 0?   f@p$ oL!?"0@NNN?N)I,$ 0 =3 (2E33?   ft$ oL!?"0@NNN?N 'O ,$ 0 =2 (2E33?   f|x$ oL!?"0@NNN?N*R,$ 0 =1 (2E33  C x(|$ oL!?"0@NNN?N ,$  0 ()D(2EE33E:5  Z$$ oL!?"0@NNN?N j ,$% 0 ?."(2G,5  Zd$ oL!?"0@NNN?N We,$ 0 ?."(2G,5  Z<$ oL!?"0@NNN?N Oc ,$! 0 ?."(2G,j  C x$ oL!?"0@NNN?NP *g,$  0 Vp18(2GOj  C xp$ oL!?"0@NNN?NC  ,$"  0 Vp28(2GOj  C x$ oL!?"0@NNN?N>  ,$&  0 Vp38(2GO  C x<$ oL!?"0@NNN?NJ^-,$ 0 Probability of states\ 2 G(G(GGf  C xԥ$ oL!?"0@NNN?N),$?  0 &Probability = Frequency in perspectiven'(2 G(G( G(G(C(  C x$ oL!?"0@NNN?N<X,$ 0 Frequency of cases\ 2 G(G(GGB "@  `D3jJL!?"0@NNN?N| ,$D.  0B @  `D3jJL!?"0@NNN?NY O ,$D*  0B @  `D3jJL!?"0@NNN?N#R ,$D2  0 # C xx$ oL!?"0@NNN?NM j ,$,  0 s1p1b(2GfOfGO $ C x$ oL!?"0@NNN?NV,$4  0 s3p3b(2GfOfGO % C x$ oL!?"0@NNN?N_ ,$0  0 s2p2b(2GfOfGO5 & Z$ oL!?"0@NNN?NV ,$3 0 ?."(2G,5 ' Z$ oL!?"0@NNN?N ,$+ 0 ?."(2G,5 ( ZD$ oL!?"0@NNN?N" 5  ,$/ 0 ?."(2G,< ? s BCDEF3jJL!?@"0@NNN?N Ma ,$D; 0 )  0e0e    BCDEFf o L!     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||@ @` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abvJ a ,$D5  0B +  `DoL!?"0@NNN?N I,$@ 0B ,  `DoL!?"0@NNN?NI R,$@ 0? -  f$ oL!?"0@NNN?N; [,$ 0 =3 (2E? .  f0$ oL!?"0@NNN?NL <dl ,$ 0 =2 (2E? /  f$ oL!?"0@NNN?N ,$ 0 =1 (2EB 1  `DoL!?"0@NNN?N @,$D 0 2  0e0e    BjCDEFf{ o L!     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||je @` "0e@      @ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN 5%  N 5%  N    5%    !"?N@ABC DEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abo J*,$D   0B 4  f D3jJL!?"0@NNN?N - ,$D   05 5@ Z$ oL!?"0@NNN?Nf ,$  0 ?."(2G,3 6 Z$ oL!?"0@NNN?Ns,$  0 =I (2E5 8@ ZT$ oL!?"0@NNN?N ; ,$  0 ?."(2G, *  f$ oL!?"0@NNN?N ' ,$ 0 F = (F1, F2, F3)(2EEEMEEMEEME` 9 # l$ GH۷oL!?"0@NNN?Nb _ ,$D  0 X For case 12 (2 EE` ; # lD% GH;۷oL!?"0@NNN?N#,$D'  0 X For case 32 (2 EE5 <@ ZX% oL!?"0@NNN?N > ,$6 0 ?."(2G,t = 3 H0e0e    BCADEdF,A Ao L!     ?1 d0u0@Ty2 NP'p<'pA)BCD|E||AS?XrV:&c  n 31Fea"@        "0e@     @ABC DEEFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `abN E5%  N E5%  N F   5%    !"?N@ABC DEFFGHIJK5%LMNOPQRSTUWYZ[ \]^_ `ab  ,$@7 0 > # lD % G4>H|۷oL!?"0@NNN?N2cA ,$D9  0 F1s1p1 + F2s2p2 + F3s3p3(2EMGfOfGOAOEMGfOfGOAOEMGfOfGO5 A Z% oL!?"0@NNN?NY 9 ,$< 0 ?."(2G, B # l\% G۽H۷oL!?"0@NNN?Nz2 ,$D>  0  p(F) = p(I)V (2EEEE$H  0޽h ?_P9:;>B ̙33@8___PPT10. /+uD,' `% = @B D' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D ' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*+%(D' =-g6B fade*<3<*+D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-g6B fade*<3<*,D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*.%(D' =-g6B fade*<3<*.D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*-%(D' =-g6B fade*<3<*-D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*/%(D' =-g6B fade*<3<*/D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*1%(D' =-g6B fade*<3<*1DR' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*2%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*2D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*2D' =%(Di' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*6%(D' =-g6B fade*<3<*6D' =A@BBBB0B%())))?D' =1:Bvisible*o3>+B#style.visibility<*5%(D ' =%(D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-o6Bwipe(up)*<3<*4D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-g6B fade*<3<*8D' =%(D3' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*3%(D' =-o6Bwipe(up)*<3<*3D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<**%(D' =-g6B fade*<3<**DF ' =%(D ' =%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*5D' =1:Bhidden*o3>+B#style.visibility<*5%(Df' =A@BB BB0B%()))D' =-g6B fade*<3<*6D' =1:Bhidden*o3>+B#style.visibility<*6%(DY' =4@BB BB%()))D' =-g6B fade*<3<*4D' =1:Bhidden*o3>+B#style.visibility<*4%(DY' =4@BB BB%()))D' =-g6B fade*<3<*3D' =1:Bhidden*o3>+B#style.visibility<*3%(D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*D' =%(D ' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-g6B fade*<3<* D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-g6B fade*<3<*D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D_ ' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*9%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*9D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*9D' =%(D' =%(DP' =A@BB5BB0B%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*9D' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*9D' =-g6B fade*<3<*9D' =1:Bhidden*o3>+B#style.visibility<*9%(D_ ' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*:%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*:D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*:D' =%(D' =%(DP' =A@BB5BB0B%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*:D' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*:D' =-g6B fade*<3<*:D' =1:Bhidden*o3>+B#style.visibility<*:%(D_ ' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*;%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*;D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*;D' =%(D' =%(DP' =A@BB5BB0B%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*;D' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*;D' =-g6B fade*<3<*;D' =1:Bhidden*o3>+B#style.visibility<*;%(D~ ' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*'%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*#%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*#D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*#D~ ' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*"%(D' =-s6Bwipe(left)*<3<*"D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*%%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*%D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*%D~ ' =%(D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D7' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*&%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*$D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*$DR' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*)%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*)D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*)D ' =%(Dz' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*<%(D9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*=%(D' =-u6Bwipe(right)*<3<*=DH' =A@BBBB0B%())?D' =.W7 BBBBBaM -4.44444E-6 4.44444E-6 C -0.0309 -0.02894 -0.0618 -0.05764 -0.08941 -0.07639 C -0.11701 -0.09514 -0.13854 -0.10371 -0.16545 -0.11204 C -0.19236 -0.12037 -0.22812 -0.12431 -0.25069 -0.12616 C -0.27326 -0.12801 -0.28142 -0.13125 -0.30086 -0.12315 C -0.32031 -0.11505 -0.35347 -0.08727 -0.36736 -0.07778 *3>*B ppt_xB ppt_y=H0BBaaaaaapBB<B<*<D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*>%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*>D' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*>D' =%(D' =%(DP' =A@BB5BB0B%(D' =+4 8?PCB ppt_wBCBB*Y3>B ppt_w<*>D' =+4 8?PCB ppt_hBCBB*Y3>B ppt_h<*>D' =-g6B fade*<3<*>D' =1:Bhidden*o3>+B#style.visibility<*>%(D* ' =%(D' =%(D9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*?%(D' =-u6Bwipe(right)*<3<*?D*' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*A%(D9' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*@%(D' =-u6Bwipe(right)*<3<*@D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*B%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*BD' =+4 8?RCBBCB#ppt_hB*Y3>B ppt_h<*BD' =%(DA' =%(D' =A@BBB B0B%()))D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?RCBBCB#ppt_wB*Y3>B ppt_w<*D' =+4 8?\CB#ppt_hBCB#ppt_hB*Y3>B ppt_h<*++0+:0 ++0+:0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+0 ++0+#0 ++0+$0 ++0+%0 ++0+&0 ++0+'0 ++0+(0 ++0+-0 ++0+.0 ++0+/0 ++0+50 ++0+50 ++0+60 ++0+60 ++0+80 ++0+*0 ++0+90 ++0+90 ++0+;0 ++0+;0 ++0+<0 ++0+<0 ++0+>0 ++0+>0 ++0+A0 ++0+B0 + 0 ((  ^  S P<     c $pPH .*    H  0re"f ? ̙33rP W#G)q[.qv|DaO< b uQ wOh+'0 `h  דילמת האסיר Samet Dovs333Microsoft PowerPoint@ @C @t~n!@ E#`Gg  0  y---$x x ----$ xx ----$x!x!----$!!x)x)!----$))x.x.)----$..x3x3.----$33x6x63----$66x:x:6----$::x?x?:----$??xBxB?----$BBxExEB----$EExIxIE----$IIxLxLI----$LLxOxOL----$OOxSxSO----$SSxVxVS----$VVxYxYV----$YYx]x]Y----$]]x`x`]----$``xcxc`----$ccxgxgc----$ggxjxjg----$jjxnxnj----$nnxqxqn----$qqxvxvq----$vvx{x{v----${{xx{----$xx----$xx----$xx----$xx---'@Times New Roman-. 2 ,0Probabilities:."System9-@Times New Roman-. $2 8'frequencies viewed .-@Times New Roman-. 2 D2in perspective.-@Times New Roman-.  2 Q A. .-@Times New 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Samet.-@Times New Roman-.  2 Qc,O.-@Times New Roman-.  2 QgD. .-@Times New Roman-. 2 Qp Schmeidler.-- @ IZH  -B( UUUU--08\\]]]]]]--  @ IZH---$[[--f-- $[[--'@Times New Roman-. 2 +3Probabilities:.. 2 *2Probabilities:.-@Times New Roman-. $2 7*frequencies viewed .. $2 6)frequencies viewed .-@Times New Roman-. 2 C5in perspective.. 2 B4in perspective.-@Times New Roman-. 33 2 O A. .-@Times New Roman-. 332 OBillot.-@Times New Roman-.  2 O&, .-@Times New Roman-. 33 2 O*I..-@Times New Roman-. 332 O0Gilboa.-@Times New Roman-.  2 OD,O.-@Times New Roman-. 332 OJD. Samet.-@Times New Roman-.  2 Oe,O.-@Times New Roman-. 33 2 OiD. .-@Times New Roman-. 332 Or Schmeidler.-՜.+,D՜.+,$    }On-screen ShowSamet  DavidArialTimes New RomanSymbolComic Sans MSDefault DesigndProbabilities: frequencies viewed in perspective A. Billot, I. Gilboa, D. Samet, D. Schmeidler"Where do probabilities come from? 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