From e38bc2a695db88e3fde7a1d39210420bda796ba4 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Tue, 11 Aug 2026 08:53:08 +0200 Subject: [PATCH] [PS] Add some remarks --- .../04_joint-distribution/02_remarks.tex | 8 ++++++-- .../probability-and-statistics-cheatsheet.pdf | Bin 1130188 -> 1130672 bytes 2 files changed, 6 insertions(+), 2 deletions(-) diff --git a/semester4/ps/ps-jh/parts/04_joint-distribution/02_remarks.tex b/semester4/ps/ps-jh/parts/04_joint-distribution/02_remarks.tex index 3b3603f..6f75656 100644 --- a/semester4/ps/ps-jh/parts/04_joint-distribution/02_remarks.tex +++ b/semester4/ps/ps-jh/parts/04_joint-distribution/02_remarks.tex @@ -1,5 +1,6 @@ \subsection{Tips \& Tricks} -\shortremark Die \bi{Dichten} können anstelle der Variablen in bspw. der Formel für bedingte W. verwendet werden. +\shortremark Die \bi{Dichten} können anstelle der Variablen in bspw. der Formel für bedingte W. verwendet werden! +Dies ist besonders nützlich für die Berechnung von bedingten Dichten, etc. und Bestimmung Unabhängigkeit \howto{Randdichten berechnen}{ \begin{enumerate} @@ -14,7 +15,10 @@ Die Randdichten sind dann die Dichten von $\cX$, etc.; Für weitere Berechnungen \howto{$cond$ auflösen}{ In dem Integral sollte jeweils der äussere Integral der sein, für welchen wir volle Information haben. Zudem, bspw., für $0 \leq x \leq y^2 \leq 1$, wissen wir zwar für $x$ und $y$ die Grenzen, wählen aber $x$ als inneren Integral, - weil $\int_0^{y^2}$ sich schöner auflöst + weil sich oft $\int_0^{y^2}$ schöner auflöst. Der äussere Integral ist dann auf dem ganzen Intervall (also äussere Beschränkungen). + + Für einen einzelnen Integral wählen wir die Grenzen als die umliegenden Grenzen. Falls wir nur eine haben so müssen wir auflösen oder eine Grenze hinzufügen, + siehe Randdichten von bspw. Einheitskreisscheibe. } \howto{Gemeinsame Dichten finden}{ diff --git a/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf b/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf index 2394acd7e02bde24bd4f6b7c9ce82d8b202c85c8..86bdd10efe5b88161ca8d02be08a67d3f1ec0a9e 100644 GIT binary patch delta 46640 zcmV(~K+nI-{Y0>VMX+)Z0yZ(1fkgo-e_eOnww3Sx6_dBosRtpxLFZ(SH_|KY{SFE4+1fAI9> zgTFnX&`CCQ7ay!q<%;ypesRy!Pc#u-t1wqQ8`-uj}ytwe0g(OR7l=JM=k(xB@rM0HiIF)o7r(5Sd^52llU0^gU^V8 ze`O<{`TKbmy|%;e=WQuf@)4@aKI>+IpA>p2)2hQ3fR34o*Bv*pHX5I=L#2+ zNdvfDbx=Pzoju@^D4D}<)eoU7t_aI=ZkmViL`ew;yzbq9Qo?X*KP(?sL#@4M6+BJv z4&nv|_W*jTVRet}1l@e9iPk^E=hdgs%f;-$+u4Jk>>9ULwOn<(e_4R0bS44YG;S0& z$lO2w_tVQ+xry?@PwS_d`)@M~npK3;L)9)xlt2+P8iEUuvhws(SoEgt>jme0{@pbY zsB1VHWfP%-7J|=PGH62qnEDu05AbNfXGRLI6?DZI z$+*)8w*(*`@cUilxKc)UI@-dN;cCJq-Il4rn>wT6?# z*oi$;KSocRVbDZoc;MhCjh=5j#vqdd(mrmY!3Zh5&O>0IH*u6(TT1$f~VHZTh3iXVQa)p&L+^DQG 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