From d02ddf44dc8b63524c9c442894c80c0470a9dc1e Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Sat, 28 Feb 2026 20:47:26 +0100 Subject: [PATCH] [PS] Fix more errors --- .../00_basics/03_properties-of-measures.tex | 2 +- .../00_basics/04_conditional-probability.tex | 2 +- .../probability-and-statistics-cheatsheet.pdf | Bin 283246 -> 283248 bytes 3 files changed, 2 insertions(+), 2 deletions(-) diff --git a/semester4/ps/ps-jh/parts/00_basics/03_properties-of-measures.tex b/semester4/ps/ps-jh/parts/00_basics/03_properties-of-measures.tex index 67dd950..f8795eb 100644 --- a/semester4/ps/ps-jh/parts/00_basics/03_properties-of-measures.tex +++ b/semester4/ps/ps-jh/parts/00_basics/03_properties-of-measures.tex @@ -26,7 +26,7 @@ Sie sind nützlich für schwer zu berechnende W. {\centering $\limni P[A_n] = \P\left[ \bigcup_{n = 1}^\8 A_n \right]$\\} und für $(B_n)$ mit $B_n \supseteq B_{n + 1}$ (mon. fallend) gilt:\\ -$\limni P[B_n] = \P\left[ \bigcap_{n = 1}^\8 \right]$ +$\limni P[B_n] = \P\left[ \bigcap_{n = 1}^\8 B_n \right]$ \shortremark Mit Monotonie: $\P[A_n] \leq \P[A_{n + 1}]$ und\\ $\P[B_n] \geq \P[B_{n + 1}]$. Grenzwerte oben wohldefiniert. diff --git a/semester4/ps/ps-jh/parts/00_basics/04_conditional-probability.tex b/semester4/ps/ps-jh/parts/00_basics/04_conditional-probability.tex index 9ec96e1..48bfbf3 100644 --- a/semester4/ps/ps-jh/parts/00_basics/04_conditional-probability.tex +++ b/semester4/ps/ps-jh/parts/00_basics/04_conditional-probability.tex @@ -12,7 +12,7 @@ \forall A \in \cF \quad \P[A] = \sum_{i = 1}^{n} \P[A | B_i] \cdot \P[B_i] \] -\shorttheorem[Bayes] $B_i$ wie oben, damm $\forall A$ mit $\P[A] > 0$: +\shorttheorem[Bayes] $B_i$ wie oben, dann $\forall A$ mit $\P[A] > 0$: \[ \forall i = 1, \ldots, n \quad \P[B_i | A] = \frac{\P[A | B_i] \P[B_i]}{\sum_{j = 1}^{n} \P[A | B_j] \P[B_j]} \] diff --git a/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf b/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf index efbd22abae44ea69347610e2a46b1b1e9cf56494..32e71518882945872a49d949ec1cdf0a8d7feec8 100644 GIT binary patch delta 4161 zcmV-H5Wes3q!I9>5wKnf0XLUHI|M0{hzSxWW@nSxq}$GBPP<7ryPNhwv1wb0EN5i7 zo$br~^}QDWNq_<T_E3zGqNlMxI) z7NMZLmxcs5*69QW`mUYS%+6}oOzXRoWegwz)suz{iGO~@^J@Qh%;O4doR+fxxcWBs z0Q{R{tH>}$p4WDy?ekhsYv*xo@iZZ|Nd|1WjN$#Ekj1OT#npWFba{b{)lAoOcu3Rd zO-f+FGj0zTV<<^z_^00W{q9jc2g!u5;q?V1w|HJ@h{moTooj(-7XrC-y|2p8#uK zE^nShOMl70-E*PvC18(nyn&*^szUj*6;8zPgR-qb z`PQIMcaP||quDavX{wt}#6;mKHuy#Zol+7GjG`W%za)kN*<2xBwXN*1#!WOq!kOLm z6eKkiTQ~ruIH11UIA;-|2ZL51faP#VWJl#7pnsiS)*WZD#S|a~a=&rPZyX=7aWq(S zrU?g86i8edY6hL}1+2LxnRTNtLCRD**&~7#b;w3^_ym6__XGbLi)k`!Dyh|sG$@2# zXny58)B(JPa9}z!AnuCCD-hx)928B;(#sT!#Jt~5|CCxfDoLRP@Q$)pbdsoVVGLJo zk&}!L&=ZG~z}{GUlYzrZ#bk!8vvj@x)01xx7k@uxdDMCG%Oo8Gl9>`%ksPp5?e&z8 zY%fN_BS-eHQtLClNbT!1A^OllL`#ZnhttQ7DxA$5Qj^mT-oLO;gX#N>B?#fOz$o!~ zEJn(&jOj`0a3CzdDM~na)SSwnB&ldopjvs$f+v@M1(~us)WA_Q-J6AV+W@0|2T}#R z`T0pNLPr46JICrg^B&BV8bRQ%lS>dV2CDV4+WfMUfe^zWk7@g~;M1!`+LeRv^1d+r zhxDv-3Mhb`8bmfj#I1kKlVlNB0j!g}5gq{oliLv;0k@O+5i9}rlO__3f4_o#UNkmI zm=}53Z;qU4SRuQXqR4xb5}f<#yLXG_8PJUE)J<=kMJA-BiRCD}dTCi6k0-ZY%ZS-> zAipp!$ZBb(0vPSQMp+0tP5Jq0AF> zwZrVmjSCesL>_Z*L0cHJf47{=sWsWkPq4Q*N>bj!plP5M33*F&z5fIcZ2^Y3`K zSubWpOdaGQu0y8&G4U;+9_1;aDcT=wZ$hCdD?q2lFfQ$4>==Q&&u+dotgWx#5igo) zV@0P(H2dHAE(vsxF60Rdi<<`{1QK9g1% zQUQUJsTqs`vy(O&PXVfvh8k1>*^}EEu>wDQla3oa2)$3?T+iSA;*-)FQvz?ZlP4V1 z0lJg?9HQzmv8drvmR+lV2XN0-tS@5g$7Nm$OYDc>#Y{ zq9Y+0d6pz2QtCa)NK!Bc9givX`Ib|CkcaO|9;Tcqy~EH~H;T)tQZ`y1ZU;L=9&V9! zJ43&gheL>8))yXGSH<;ek&I$Fq~J+(-w5IfA1_dU5@$eC_{I>DF+y=SGhfo3CX_f& zq}-BYv{8qI4?RnpfP~s#)=KY#Jd%Gu=vjInBpoA6WcESsFlFIZe6_Atzj(9C#@kJ< zePs%tD`($cUoOuojPzdN)uQQ=z6$!sE6FgiXw`o!nIWuuEm<^OjYZ^y2EJ{G;QA1`B@@Gz zVuvs&Rq{boyLXxzr@~&I-OmwyqmHH~Msvh=umd!;09m(>kJr>9i1#}^s(X6&C24I; zb?WG`5=1fn;5@v)M-UU^jOagszD>tzuA;S z+)o_qoOYX(GWx*hq(pyxAD_ONy&RZMNLiL(*uo0xfnwZaied1+qaEhex>1K_sL?c| z9qbUI(PC{fkWvyXcpHL@r~mbd;nVBQ9ItM|g7t4m{>B+ieGM00$V?3vUbK$A(D-HC zO&Yt4xWpAcFeT6))@*-DAkU@*wnc2ZDS_R3s;gv{Wm)juHCSAg|D-=vkTNz3rY@3h z1KE6|8@CNuALPVdFYv7mPOu4{GiP031y&a6*j+b^jSYz9oCXy|x^$0b@Bea?p7v<` zG&xP!SW%dr^HeqyE?c{$O;E#cHQXbI#T`GM})7olLgh5-qy=k5|vr< z?gM_*RKVe4f$8@hM01`gPMD;z^B}zhi=OM6qM8F^u1^CB@57V5BpZLJ6UTLZjAgWJ z?|hedPmU3MQ4-cEOEMguj?2bhLc=JMFW%>}G0;+W?*ECTuC^~2Q+IYs^yfUSd>&gE z*Y`dpi{V90IdQBMM@V!!29k8pKdz#J7uak|V|R)qd%)8z!w22jVv$&eueqc{`7o64 zSMzt5L8YkG#o}UD=n0coB^!UZAsFlcaV<)X-0s^cFUp4~`Vcn$m;1 z*hh=AJWgalaaV=8232>s8zpvl1OerSpceKJL2%y`Q7X`SzM~>d-KY~mFuJNkFxVlK ztwq*UNS&}TuOY-QteHDUd5%|qtJnURyGnH2UG3S+R|l(ov5hz_AnpvJ{N;8fwqww4 zij_B${UsZJ%QGa)7%qgQHJ7%n>~(bb%Z*LT$JaO2@*P&>#;0wb-$C%Pz9u1mub3YYR+b2F7v|II@3)Je=F4ied9qbU-9$y? 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