From c2caa431d886c6449f83ba71e784e20d14a71a03 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Wed, 19 Aug 2026 11:18:59 +0200 Subject: [PATCH] [PS] Fix Log LH func of poisson dist --- .../parts/06_estimators/02_max-likelihood.tex | 2 +- .../probability-and-statistics-cheatsheet.pdf | Bin 1135521 -> 1135515 bytes 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/semester4/ps/ps-jh/parts/06_estimators/02_max-likelihood.tex b/semester4/ps/ps-jh/parts/06_estimators/02_max-likelihood.tex index 0157429..9593eaf 100644 --- a/semester4/ps/ps-jh/parts/06_estimators/02_max-likelihood.tex +++ b/semester4/ps/ps-jh/parts/06_estimators/02_max-likelihood.tex @@ -67,7 +67,7 @@ $p_\cX(x; \vartheta) = \P_\vartheta[\cX = x] = \vartheta^x (1 - \vartheta)^{1 - \highlight{Poisson} dabei $\vartheta = \lambda$ und \bi{Log LH-Func} \[ - l(\vartheta) = -n \vartheta \lambda + \log(\lambda) \sum_{i = 1}^{n} x_i - \sum_{i = 1}^{n} \log(x_i!) + l(\vartheta) = -n \vartheta + \log(\vartheta) \sum_{i = 1}^{n} x_i - \sum_{i = 1}^{n} \log(x_i!) \] \bi{ML-Schätzer} ist $T = \frac{1}{n} \sum_{i = 1}^{n} X_i$ diff --git a/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf b/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf index c87a45ac31462565e88c1a718fe186a99533734f..0cb01e7a17242d556b1429502f9a34405a8a7e9e 100644 GIT binary patch delta 7207 zcmajb!I^(mhf}cY}1-kS?X0kt0P!Ng1M~NIl>C2i}L@ zJ?EZtKi!HtmEt-TXzMA8xJZ75DmrJ!=BYeAIPrJTtg}T&%qP$0(|RF1YHRThtEd1h zokx)^rr*yaxV!`$P+a4DC(Ht%?cSXN}71inSv)Vfzn@je0RPeP?Rz#HCLa zGi}|-cEP9w?*k{#tbMh;GS%>@dH3I49J8_7Fj|FPh!9bVNSVkhj;bw$$Tg-?$1B6`|6_z}IplT#jxfwlx;A4;H;s&2>3bR}wS z9ObMIR-~M+`JGG3tpR3WH1);WG-R}HPVYb=AcClx_FZ`V-)}%-pqX zyOqf+{v8D7;&6{`tj{jLWoSk*^&kuC56}0G7xH>>57d98Ld3ucK5c2*OP>=R$gKr= z@s2rO8Fw4~e00!6Y66rNonVT9DIk?;Tq8-$^iL$~yMnl9e&*>>Zq41S7{fFa$fGS1 zSnI^0OYgCYQ(oD%;u_bDJQEsZeQgMVc9E6}0t?4co%NE1yO0x{5wR6VH!kX9X|dz0 zTD^Q~WObW914wm3D<%wI`yopx-40X(kPv+gd5qHORGQH^8fJMNHc4LahcPBr4PMVU zDt!XQWbKhda#w9J#kBZbRyb-w_-0o`Q zP$;pZhKezu<~c-nk1K{f@?Ztca`@A$j@rMhzD=R{EVE?+yBAMa_hILV`+)!!oJN0pP=!?KF#`|7#` zwnjU3a(8*abJ$RT$6?~pl$hx@W6QxP(?&qgA_r=4{PZ!Izj;Oc{WXvvq1|TQ*R%9= zPxT>ninsx@PyQUd-_0AsTy+fa+B6d*A4qGKvGYsq%e?vxMxDXkboOOGgT(@Fdc;O# zzX!%R2UeE-LNDZ)|0vC==W2$Zr(lc|Fg&*YYJ)v0vBW5d4S?01y)M1bfH^2=krJgO zh^dCpsOq-4Qzh#Eifnbkc1$NYH$D+5uTU z13N}N0Vhk}BU!ME!1jO$>PZYuygo)sR*f)?o&ZhypD|A0IEf|RhfHFcMJ!R~z8xwu z0tn%b?EK-Ap*1*)>ojDP+`rOa=A#=j3;XeTwvdQvv14JvIvf^8BR%scHF@mNCu26L z+TT17^fxa4w;?4)GpAfRyWokTE7DdJqibAZQr`R@^X9?!-?gwx$+-=Ma17g6nbGNJJU z(H$joEn~Ke2ZbrsvDqQwHy{Rl`tJ^)VPGS(QRu4=xG#nla|& z2Ai`xMqc**WG}6HKh-7afBaRhBWpXSn5W9l7-fyIvIg37D3Uxq=S=X+#AWXf;Iz*p zkkq9o2wutt?EBa7bvj+}7PxJWJb61@SAtD$ZCOUFfeV=X4yIH~T8?_i>#e+lPVE6_ ze%}X(jf+EyB)eL-@&0fZH(D<>{6H6!B5TT42W{H4)AI!EVJNKT(O6(WZFQbq3W=J?CEx`g{5io?yZ|J zX6=o_frUPeFu&uQvc>#4Pqtt{{){ZgAjz=Q>34tbDYWGanVYHF8MhpfXf9QOcIOS~ zwp!x`>Q-yRmCKizd`}WU<@Pi9Un2e=`Wv>8{!92R;mbh1GCmRAZ&Lx@tRN z+L@UADPkB^%pc>QETA0scdFU00)YmJw38pzP0lNaENHLtXurV8gDi(zM9uEE@FwZ% zGh7&`K5Zv@s1#}&=_%Nzz`?du+!U%O%|cvIqfstY0-}?w8beWUp)i-pa94d}u@yOL zVTNOyza&11$9kc8>rEAId&F+3mSLmJCER2^$0arU6_PDJ3LM#-9a88$rTN_sGXxU3 z85VMuT{=Q+M%OLtEHh3^G&Mt-g6?UB_WSQTyFYYjFqkx7%9gafol?4H>d^pBUZ8Ue~ z&+DdpH&O8WJeeOIOyIzbZ(q=Z)_M!8K-=^!r>`^37_BKQ*zPuHvd|~7q ze%xw6n#r4WQSyzFJ5Eq{&an zTKpIdp~5#JR^&*WK0nU&r}grkb}JbfWP{hvnnl?qEk8sejZK3EpHH8{(NjHU`3i-f zk-}iY##$B{Vp|QyuCr^+hEA@zge_T&uJ8nvCNm!zs#@dr<(W=5xoKdh8)114k9D>2 zc|+P*4YQv)1}m z2aHR@u= z+RCUh?tPU2c?)3=d4KPI#WiND$eG5dImo85KZ`e)#thiXoa!o5FH$d#KFf%M&8BD94*`3U9P%W?ad$RM|K*ED(uitgdQ(!@#zr?`o8n zwyod(wNE}w1d?d&;V8>sMToim;H$;Wb&@}AJn6@_d#yc%V`Al*i!;4fVZT{!$XhOI z^m6FuO$Bzutum80_bo$|e;Md@(;S@`dxM}`42#-|aR-+NcqLC&w`i;;WW->&Ij<^B zFTFv_r^}7K0jQ?J#kJN%yd#Q!@kouf9Wek4YkQsQH`t?t4oYcKl(6%z`sThGn6wln zwfkz9E+Jmggo|yM{c^e&(QFZUmGt7m`ZDZs@EM#l>`q^9TCvbTars1aywrpt&4td! 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