From a957a202445e8b648f9727e1bf6c2a9f4648dd6d Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Tue, 14 Jul 2026 14:44:55 +0200 Subject: [PATCH] [PS] Small note improvement for estimators --- .../ps-jh/parts/03_expected-value/02_cont.tex | 2 -- .../parts/06_estimators/02_max-likelihood.tex | 2 +- .../probability-and-statistics-cheatsheet.pdf | Bin 1121812 -> 1121817 bytes 3 files changed, 1 insertion(+), 3 deletions(-) diff --git a/semester4/ps/ps-jh/parts/03_expected-value/02_cont.tex b/semester4/ps/ps-jh/parts/03_expected-value/02_cont.tex index 0974e88..dc3c96a 100644 --- a/semester4/ps/ps-jh/parts/03_expected-value/02_cont.tex +++ b/semester4/ps/ps-jh/parts/03_expected-value/02_cont.tex @@ -6,8 +6,6 @@ \shortlemma[Int über gauss. Glockenk.] $\int_{-\8}^{\8} e^{\frac{-x^2}{2\sigma^2}} \dx x = \sqrt{2 \pi \sigma^2}$ \subsubsection{Beispiele} -% TODO: Consider if need derivation of them here and prev section as well -% TODO: Also add the ones proven in exercises \begin{itemize} \item $\cX \sim \cU([a, b])$, $a < b$: $\E[\cX] = \frac{a + b}{2}$ \item $\cX \sim \text{Exp}(\lambda)$, $\lambda > 0$: $\E[\cX] = \frac{1}{\lambda}$ 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 23a1e22..7091bcb 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 @@ -40,7 +40,7 @@ Meistens sind $\cX_k$ i.i.d. unter $\P_\vartheta$, dann $L$ produkt, also besser \begin{enumerate} \item log-LH-Funk. bestimmen ($x_i$ statt $\cX_i$ verwenden) \item Nach $\vartheta$ ableiten (oder wodurch $\vartheta$ ersetzt wurde) - \item Nullstelle davon berechnen + \item Nullstelle davon berechnen (für Max (via e.g. $f'' < 0$)) \item ML-Schätzer ist dann Nullstelle von Ableitung (mit $x_i$ wieder durch $\cX_i$ ersetzt) \end{enumerate} diff --git a/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf b/semester4/ps/ps-jh/probability-and-statistics-cheatsheet.pdf index 85966bc0780eb95bfda7f8d0dbf351adee498064..fbe238bd0f984fa76e8aaf9a7d5f6d83b835407a 100644 GIT binary patch delta 42818 zcmV(*K;FNUyhNG2M6ehVe-s3VRP!Hh)~j-GmN6A9t6eT=$b~AQ$T?9N%v-=lh}cHV zUN0y`Oj};BPOl@KH9%!B8AA|x%YI0_r~b{j-kwl4|NDvLX1=_+EGpb?VIdciP$dx! z|2l&qzMI)`9#~A2fQtAS{)5kmfq!bYg|}aSIDh-Er%Otp?KQk4e}ZaGXK=14mpPzr z{Rno2DGErv4xSmx7@tvM6z2*Tl1T$7U3E}DIGsJ$O4%ZK%E3OF3a&DT3@I*-o z=eq9Qe^SD5YCkL=Rzt15XB9k6?+)Sy2KNAZs$q4H>;&C>s)^P=!{^nf(96Z_!Q0t` zpX?g9R<&GpyIFvpe{?1R+ca(zHptvR|M%0&S-FYvBVKj3U>S4=1c=LwNXoEFOIiR6 z8`9z$Rc$OLJ}J((t6wt8dr6FkWUWqMpr4vaE$plo^|XGPx&Jn^pjkyPJyh*dLJ5R0 zqanBeDJu^>g+*`LzFu(7=ihCCE^Xmxlud*RS_nRWSiZ=0f9KP$T(4OczM_2Y1`J?( zy=P zGH62qnEDu05AbNfXGRLI6?DZI$+*)8w*(*`@cUilxK zc)UI@-dN;cCJq-Il4rn;wT6?#*oi$;KSocRVbDZoc;MhCjh=5j#vqC$j<|phIFElQ z=L=-D2=ED=zc~T%V7q*HVtahMT(7Smb(wq9!2(c~e^F{Bwp=;1L)skW939B#Hyy5+xuq;x?OI543r9t4k`fo^(bx(_xQXQlQtlDrE%$T^1J2D z=|$CXe-dL%2C^V;?H%8L?{ev_I@5%Mm1dA#R?s0E z(cvTfp~@fl*Jxx@ep5-UzNCrJP6T*S^+-L44dK9S7C_Y%57)rQPdF`_4a*KHM>y&{s2nxK6!EQhZFgyl(00FQm6Tp52D{AIv#dg$apr&#j!~1;) zvpth?!AQAa?gwadC)F|mi?J(JQ;DuP$dmwiMeZREn%QU8-9QeL88ar(-B4JQ9E9}d ze^dB2v9_n*|dTm7&l3YHB$QLya2kp&$L|4h0Y1NO-VbhoNask>c&7%2^ULmZ&B zdDvNMZMr263K;^Lmb}#5iHUH6w#B9tx!%|VRjkUt=-*B(%Y9{SQ3j4H6=-Rr+|lvB z+ZXTzNrm_PX8X2SyDmM78Hiz}2xiIef46B)^)~uxl#~J4jLEM^5!k5qdd^3-7bD@3 zBl}m;1)877c6J^SfhcGRK4;6|9OlR`1yTryDWFESKWl9Wib2n!K%yeiw~OEOO}PC9 z&iH=c`}Y03cYj-&$!%`zWR-F5biA`=O>&aT!n(3eP6y3niswZEmcxm|%rja+;Ek3rFa zZlW&QvGY9TAw{S~mXJ873C}U`_lRq_V2sUQmp=|i&ILDlf>WR5K5D!^BudkK|SPWs5VKv3j78%d++ zuW^~onEB;umn1ij({Spq5)+4a(TM}#v0-FwpAK99n$%(euFchMRcv?hH8Q5whQ~7b zxRjXZ^B%R@TI84p+-R{hf9pCm ziF4QS+TIM5d{dhNE00U`Yh@C&?1LWUffXv^_f7b3dUdpDqzNDju$;5A)o%40;A|5g zwu|ASPJsQaj?|cL%Qxfil%!leShAMF@GM#m>+dihh8{af9uhczDIA`%zbF6 zBA`2!4kQtRuk1()1rE1D0Z2B7jvGy_biTeL)`9aDl_H zU`13J=~uPF19!H%es{BZzjO5Fzff#OwSBWXzuBDkIO7a#SQ#jM?~A)DzBpru%4x4? z=9*0O#5DsP;D~E5f3t*Ab^UNYl&@BW^-?4Hqkv<7Dcx!^C!mmxcB^3+cvA8FJ#6`+ zwp(%(L;FpZ3k_>zS5stZi)Dm=KYsIOwLSx?k)FKii_b_#!_+|_ZPrY)JUw;!*p{xtv?WuKXPPi^D`^FRp-8n~3ZcN--#Up%epzO3_vv zQ@G)*4?9Bk4x$m)K70QV`4-TR@)&y$_6XZ|xO;RvVq+L$j2=IR=OVQGZ>?_It2e|+ zY1&vRDv;9te|LGYP6}zOWZ>e*GU*1m0A}6nO_9Gz4i#GlF6?OoU~3{LM)y$y=tk2%LQr*t$w59LXrDVwEl?;QaJL`vGrQ`e$-|NV zi6G?0^g0tD5oh~`tW-hAtJ)Fws_Mj`du?BI=omJmf7xN)MoYBf%_IXFQHRJvF?QxTp%Qqolm;|Boe-&AtE$mxb7$-ON%qbP zLl+*3c0uK^UAbz3`ilH#k{a01Po(QFPmGvvS073~vW`o~&L4emjgL7_t}MaD!Z^g#K3epX9I`WHJX@T*y?4PhTNRx23@j9Tvom~piB>klHJlFul?H4si1>vSpI<4Li){;(?61&l4s{I@I2tPy%-?SxH=hKL-{JY)Cz$z93BuE>Z0 z1i&=jUNTZOnyR39gG|WBuIY$}q%jReKu0Qs^*@#$*2_~kGeBMD&#&OrXY;dS9oIsH zHeZky60`Ipgx8pOr{`xbu&N7=Xzb~&e+ep@%=eM>kQ{Uz(sPOgA=}J=PJr<=3eFSn zaXMR?+LJiza^}BElI4S{QGZ0FfT--u4y z&S{q2Lfk^j{cV8$%VWAmgpfq$`3#6Hu=~8%If9YsI<$#~Bh;N~q!7Ij{?r3ue>WzT zWz3pTRoUgkROAS+b|7NVuI-_($a9k9yHW#N()VumJK<)pnXbaxVq$>lx<;d2?XB+* zG$nW#+I6>cEH?)G6~Ou!okTZpkzA|!pSOiAdL!~P$7r@_)t=?v; 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