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概率论中的小错误

在概率论的knowledge/law-of-large-numbers-and-central-limit-theorem.tex里面,有一个例题似乎有错误(应该是$n \ge 1$)
image


另外,在knowledge/2-random-variables-and-distribution/random-variables-and-distribution.tex有一个字打错了(性 →型)
image

期望

祝自己成功上岸 初试+复试

VScode无法编译.tex

log 如下:

Initial Win CP for (console input, console output, system): (CP936, CP936, CP936)
I changed them all to CP936
Rc files read:
  NONE
Latexmk: This is Latexmk, John Collins, 4 Apr. 2023. Version 4.80.
No existing .aux file, so I'll make a simple one, and require run of *latex.
Latexmk: applying rule 'pdflatex'...
Rule 'pdflatex':  Reasons for rerun
Category 'other':
  Rerun of 'pdflatex' forced or previously required

------------
Run number 1 of rule 'pdflatex'
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Running 'pdflatex  -synctex=1 -interaction=nonstopmode -file-line-error -recorder  "d:/Documents/Math-master/advanced-math/knowledge/0-perpare/perpare.tex"'
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This is pdfTeX, Version 3.141592653-2.6-1.40.25 (TeX Live 2023) (preloaded format=pdflatex)
 restricted \write18 enabled.
entering extended mode
(d:/Documents/Math-master/advanced-math/knowledge/0-perpare/perpare.tex
LaTeX2e <2022-11-01> patch level 1
L3 programming layer <2023-02-22> (c:/texlive/2023/texmf-dist/tex/latex/ctex/ctexart.cls (c:/texlive/2023/texmf-dist/tex/latex/ctex/config/ctexbackend.cfg) (c:/texlive/2023/texmf-dist/tex/latex/l3kernel/expl3.sty

c:/texlive/2023/texmf-dist/tex/latex/l3kernel/expl3.sty:78: LaTeX Error: Mismatched LaTeX support files detected.
(LaTeX)        Loading 'expl3.sty' aborted!
(LaTeX)        
(LaTeX)        The L3 programming layer in the LaTeX format
(LaTeX)        is dated 2023-02-22, but in your TeX tree the files require
(LaTeX)        at least 2023-08-11.

For immediate help type H <return>.
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l.78      \ExplLoaderFileDate{expl3.sty}}
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)
Document Class: ctexart 2022/07/14 v2.5.10 Chinese adapter for class article (CTEX)
(c:/texlive/2023/texmf-dist/tex/latex/ctex/ctexhook.sty) (c:/texlive/2023/texmf-dist/tex/latex/ctex/ctexpatch.sty) (c:/texlive/2023/texmf-dist/tex/latex/base/fix-cm.sty (c:/texlive/2023/texmf-dist/tex/latex/base/ts1enc.def))
c:/texlive/2023/texmf-dist/tex/latex/ctex/ctexart.cls:102: Undefined control sequence.
l.102 \sys_if_output_pdf:TF
                           

c:/texlive/2023/texmf-dist/tex/latex/ctex/ctexart.cls:104: LaTeX Error: Control sequence \ifctexpdf already defined.

For immediate help type H <return>.
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l.104   { \cs_new_eq:NN \ifctexpdf
                                   \if_false: }
(c:/texlive/2023/texmf-dist/tex/latex/ctex/config/ctexopts.cfg) (c:/texlive/2023/texmf-dist/tex/latex/base/article.cls
Document Class: article 2023/05/17 v1.4n Standard LaTeX document class
(c:/texlive/2023/texmf-dist/tex/latex/base/size12.clo)) (c:/texlive/2023/texmf-dist/tex/latex/ctex/engine/ctex-engine-pdftex.def
c:/texlive/2023/texmf-dist/tex/latex/ctex/engine/ctex-engine-pdftex.def:97: Undefined control sequence.
l.97 \sys_if_output_pdf:T
                         
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c:/texlive/2023/texmf-dist/tex/latex/ctex/ctexart.cls:1471: Undefined control sequence.
<argument> \sys_if_output_pdf:TF 
                                 {##1}{##2}
l.1471       { \sys_if_engine_uptex:TF {#3} {#4} }
                                                  
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For additional information on amsmath, use the `?' option.
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[Loading MPS to PDF converter (version 2006.09.02).]
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*geometry* driver: auto-detecting
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No file perpare.toc.
(c:/texlive/2023/texmf-dist/tex/generic/ctex/zhmap/ctex-zhmap-windows.tex) [1{c:/texlive/2023/texmf-var/fonts/map/pdftex/updmap/pdftex.map}]
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[]\C70/rm/m/n/12/5b � \C70/rm/m/n/12/4e I \C70/rm/m/n/12/57 �|\C70/rm/m/n/12/ff ^^Z| $\OT1/cmr/m/n/12 (\OMS/cmsy/m/n/12 ^^@1\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 +\OMS/cmsy/m/n/12 1\OT1/cmr/m/n/12 )$|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/50 < \C70/rm/m/n/12/57 �|\C70/rm/m/n/12/ff ^^Z|

pdfTeX warning (ext4): destination with the same identifier (name{page.1}) has been already used, duplicate ignored
<to be read again> 
                   \relax 
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                   {对数函数} \leavevmode \medskip [1] [2] [3] [4] [5] [6]
Overfull \hbox (2.47614pt too wide) in paragraph at lines 477--478
[]$\OML/cmm/m/it/12 x$\C70/rm/m/n/12/4e : \C70/rm/m/n/12/5b � \C70/rm/m/n/12/65 p|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/4e ^^M \C70/rm/m/n/12/8d � \C70/rm/m/n/12/8f �$\OML/cmm/m/it/12 x$\C70/rm/m/n/12/76 � \C70/rm/m/n/12/67 ^^@ \C70/rm/m/n/12/59 ' \C70/rm/m/n/12/65 t p \C70/rm/m/n/12/79 � \C70/rm/m/n/12/4e : \C70/rm/m/n/12/51 v \C70/rm/m/n/12/65 t p \C70/rm/m/n/12/90 � \C70/rm/m/n/12/52 ^^F$\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 ]$|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/51 v \C70/rm/m/n/12/5b � \C70/rm/m/n/12/4e I \C70/rm/m/n/12/57 � \C70/rm/m/n/12/4e :$\OML/cmm/m/it/12 R$|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/50 < \C70/rm/m/n/12/57 � \C70/rm/m/n/12/4e :$\OML/cmm/m/it/12 Z$|\C70/rm/m/n/12/30 ^^B|

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Underfull \hbox (badness 2057) in paragraph at lines 519--520
[]$\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )$\C70/rm/m/n/12/6c �$\OML/cmm/m/it/12 x$\C70/rm/m/n/12/8f t \C70/rm/m/n/12/5d � \C70/rm/m/n/12/79 �$\OML/cmm/m/it/12 x[]$\C70/rm/m/n/12/4e * \C70/rm/m/n/12/53 U \C70/rm/m/n/12/4f M \C70/rm/m/n/12/95 ^^?

Underfull \hbox (badness 8038) in paragraph at lines 519--520
\C70/rm/m/n/12/5e � \C70/rm/m/n/12/5f � \C70/rm/m/n/12/52 0$\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x \OT1/cmr/m/n/12 + \OML/cmm/m/it/12 x[]\OT1/cmr/m/n/12 )$|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/54 ^^Q \C70/rm/m/n/12/53 �

Underfull \hbox (badness 10000) in paragraph at lines 541--542
[]$\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )$\C70/rm/m/n/12/6c �$\OML/cmm/m/it/12 y$\C70/rm/m/n/12/8f t \C70/rm/m/n/12/4e 
 \C70/rm/m/n/12/79 �$\OML/cmm/m/it/12 y[]$\C70/rm/m/n/12/4e * \C70/rm/m/n/12/53 U \C70/rm/m/n/12/4f M \C70/rm/m/n/12/95 ^^? \C70/rm/m/n/12/5e � \C70/rm/m/n/12/5f �
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Underfull \hbox (badness 2253) in paragraph at lines 600--601
[]\C70/rm/m/n/12/5c ^^F$\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )$\C70/rm/m/n/12/51 s \C70/rm/m/n/12/4e �$\OML/cmm/m/it/12 x$\C70/rm/m/n/12/8f t$\OML/cmm/m/it/12 y$\C70/rm/m/n/12/8f t \C70/rm/m/n/12/53 s \C70/rm/m/n/12/51 s \C70/rm/m/n/12/4e � \C70/rm/m/n/12/53 � \C70/rm/m/n/12/70 �
[8]
Underfull \hbox (badness 10000) in paragraph at lines 637--638
[]\C70/rm/m/n/12/4f � \C70/rm/m/n/12/75 Y$\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )$\C70/rm/m/n/12/51 � \C70/rm/m/n/12/65 p \C70/rm/m/n/12/50 < \C70/rm/m/n/12/57 ($\OT1/cmr/m/n/12 [0\OML/cmm/m/it/12 ; \OMS/cmsy/m/n/12 1\OT1/cmr/m/n/12 ]$\C70/rm/m/n/12/76 � \C70/rm/m/n/12/90 � \C70/rm/m/n/12/52 ^^F|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/5e v
[9] [10{c:/texlive/2023/texmf-dist/fonts/enc/dvips/cm-super/cm-super-ts1.enc}] [11] [12]
Overfull \hbox (5.74239pt too wide) in paragraph at lines 893--901
[]\C70/rm/m/n/12/4e � \C70/rm/m/n/12/57 ^^F \C70/rm/m/n/12/53 J \C70/rm/m/n/12/5f � \C70/rm/m/n/12/4e :$\OML/cmm/m/it/12 r$|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/64 F \C70/rm/m/n/12/70 � \C70/rm/m/n/12/4e ^^N \C70/rm/m/n/12/57 ^^F \C70/rm/m/n/12/5f � \C70/rm/m/n/12/62 @ ^^P \C70/rm/m/n/12/76 � \C70/rm/m/n/12/7e � \C70/rm/m/n/12/62 @ \C70/rm/m/n/12/8f l \C70/rm/m/n/12/52 � \C70/rm/m/n/12/59 9 \C70/rm/m/n/12/89 � \C70/rm/m/n/12/5b � \C70/rm/m/n/12/5e � \C70/rm/m/n/12/5f ' \C70/rm/m/n/12/5e � \C70/rm/m/n/12/4e :$\OML/cmm/m/it/12 t$|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/51 v \C70/rm/m/n/12/4e -$\OML/cmm/m/it/12 t \OMS/cmsy/m/n/12 2 \OT1/cmr/m/n/12 [0\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 2\OML/cmm/m/it/12 ^^Y\OT1/cmr/m/n/12 ]$|\C70/rm/m/n/12/ff ^^L|
[13] [14] [15] [16]
Overfull \hbox (2.87325pt too wide) in paragraph at lines 1083--1084
[]\C70/rm/m/n/12/6b c \C70/rm/m/n/12/5f & \C70/rm/m/n/12/51 � \C70/rm/m/n/12/65 p$\OML/cmm/m/it/12 y \OT1/cmr/m/n/12 = [] \OML/cmm/m/it/12 x$\C70/rm/m/n/12/57 ( \C70/rm/m/n/12/4e ; \C70/rm/m/n/12/50 < \C70/rm/m/n/12/53 : \C70/rm/m/n/12/95 �$[]$\C70/rm/m/n/12/4e 
 \C70/rm/m/n/12/76 � \C70/rm/m/n/12/53 � \C70/rm/m/n/12/51 � \C70/rm/m/n/12/65 p \C70/rm/m/n/12/5c 1 \C70/rm/m/n/12/66 / \C70/rm/m/n/12/53 � \C70/rm/m/n/12/6b c \C70/rm/m/n/12/5f & \C70/rm/m/n/12/51 � \C70/rm/m/n/12/65 p|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/8b � \C70/rm/m/n/12/4e :$\OML/cmm/m/it/12 y \OT1/cmr/m/n/12 =

Overfull \hbox (8.34384pt too wide) in paragraph at lines 1099--1100
[]\C70/rm/m/n/12/56 � \C70/rm/m/n/12/4e : \C70/rm/m/n/12/51 s \C70/rm/m/n/12/4e �$[]$\C70/rm/m/n/12/5b � \C70/rm/m/n/12/79 �|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/82 �$\OML/cmm/m/it/12 x[]; x[] \OMS/cmsy/m/n/12 2 \OT1/cmr/m/n/12 (\OMS/cmsy/m/n/12 ^^@\OT1/cmr/m/n/12 1\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 1)$|\C70/rm/m/n/12/ff ^^L| $\OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 = \OMS/cmsy/m/n/12 ^^@\OML/cmm/m/it/12 x[]$|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/52 ^^Y$[] \OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 + [] \OML/cmm/m/it/12 x[] \OT1/cmr/m/n/12 =
[17]
Overfull \hbox (5.05315pt too wide) in paragraph at lines 1117--1118
[]\C70/rm/m/n/12/6b c \C70/rm/m/n/12/52 ^^G \C70/rm/m/n/12/51 � \C70/rm/m/n/12/65 p \C70/rm/m/n/12/66 / \C70/rm/m/n/12/51 s \C70/rm/m/n/12/4e � \C70/rm/m/n/12/53 � \C70/rm/m/n/12/70 � \C70/rm/m/n/12/5b � \C70/rm/m/n/12/79 �|\C70/rm/m/n/12/30 ^^A| \C70/rm/m/n/12/4e % \C70/rm/m/n/12/68 < \C70/rm/m/n/12/53 U \C70/rm/m/n/12/8c ^^C \C70/rm/m/n/12/90 ^^R \C70/rm/m/n/12/58 �|\C70/rm/m/n/12/30 ^^A| \C70/rm/m/n/12/67 	 \C70/rm/m/n/12/75 L \C70/rm/m/n/12/76 � \C70/rm/m/n/12/59 G \C70/rm/m/n/12/51 � \C70/rm/m/n/12/65 p|\C70/rm/m/n/12/30 ^^B| \C70/rm/m/n/12/50 < \C70/rm/m/n/12/57 � \C70/rm/m/n/12/4e :$[]$|\C70/rm/m/n/12/ff ^^L|
[18] [19] [20]
Overfull \hbox (23.49008pt too wide) in paragraph at lines 1299--1300
[]\C70/rm/m/n/12/63 � \C70/rm/m/n/12/5e ^^? \C70/rm/m/n/12/51 l \C70/rm/m/n/12/5f ^^O \C70/rm/m/n/12/4e ^^@ \C70/rm/m/n/12/52 0 \C70/rm/m/n/12/8f � \C70/rm/m/n/12/7e � \C70/rm/m/n/12/53 : \C70/rm/m/n/12/95 � \C70/rm/m/n/12/4e ^^T$\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )$\C70/rm/m/n/12/57 ($\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 a; b\OT1/cmr/m/n/12 ](\OML/cmm/m/it/12 a < b\OT1/cmr/m/n/12 )$\C70/rm/m/n/12/4e 
 \C70/rm/m/n/12/53 � \C70/rm/m/n/12/79 �|\C70/rm/m/n/12/ff ^^Z| $\OMS/cmsy/m/n/12 j [][] \OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )[]\OML/cmm/m/it/12 x\OMS/cmsy/m/n/12 j \U/msa/m/n/12 6 [][] \OMS/cmsy/m/n/12 j\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )\OMS/cmsy/m/n/12 j[]\OML/cmm/m/it/12 x$|\C70/rm/m/n/12/30 ^^B|
[21]
Overfull \hbox (8.95349pt too wide) in paragraph at lines 1324--1325
[]$\U/msa/m/n/12 *$\C70/rm/m/n/12/97 ^^@ \C70/rm/m/n/12/89 � \C70/rm/m/n/12/8b � \C70/rm/m/n/12/66 ^^N \C70/rm/m/n/12/67 	 \C70/rm/m/n/12/75 L \C70/rm/m/n/12/60 '|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/4e � \C70/rm/m/n/12/53 � \C70/rm/m/n/12/68 9 \C70/rm/m/n/12/53 � \C70/rm/m/n/12/4e ^^M \C70/rm/m/n/12/7b I \C70/rm/m/n/12/5f ^^O \C70/rm/m/n/12/4e � \C70/rm/m/n/12/97 ^^@ \C70/rm/m/n/12/89 � \C70/rm/m/n/12/53 � \C70/rm/m/n/12/65 p \C70/rm/m/n/12/59 ' \C70/rm/m/n/12/4e �\OT1/cmr/m/n/12 0|\C70/rm/m/n/12/ff ^^L| \C70/rm/m/n/12/62 @ \C70/rm/m/n/12/4e � \C70/rm/m/n/12/97 ^^@ \C70/rm/m/n/12/89 � \C70/rm/m/n/12/8b � \C70/rm/m/n/12/66 ^^N$\OMS/cmsy/m/n/12 j\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )\OMS/cmsy/m/n/12 j \OT1/cmr/m/n/12 =
[22] [23] (./perpare.aux)name = unihei75, rootname = unihei, pointsize = 75
mktexmf: empty or non-existent rootfile!
Cannot find font unihei75 in map file(s).

kpathsea: Running mktexmf unihei75.mf

The command name is C:\texlive\2023\bin\windows\mktexmf
Cannot find unihei75.mf .
I try ps2pk --> gsftopk --> ttf2pk --> hbf2gf.
ps2pk cannot be used.
I try gsftopk.
gsftopk.exe unihei75 864
gsftopk cannot be used.
Next I try ttf2pk.
ttf2pk.exe -q unihei75 864
ttf2pk failed.
Finally I try hbf2gf.
hbf2gf.exe -q -p unihei75 864
All trials failed.

kpathsea: Running mktexpk --mfmode / --bdpi 600 --mag 1+264/600 --dpi 864 unihei75

The command name is C:\texlive\2023\bin\windows\mktexpk
kpathsea: Appending font creation commands to missfont.log.


Package rerunfilecheck Warning: File `perpare.out' has changed.
(rerunfilecheck)                Rerun to get outlines right
(rerunfilecheck)                or use package `bookmark'.

 )
(see the transcript file for additional information)
!pdfTeX error: pdflatex.exe (file unihei75): Font unihei75 at 864 not found
 ==> Fatal error occurred, no output PDF file produced!
Latexmk: Missing input file 'perpare.toc' (or dependence on it) from following:
  No file perpare.toc.
Latexmk: Getting log file 'perpare.log'
Latexmk: Examining 'perpare.fls'
Latexmk: Examining 'perpare.log'
Latexmk: References changed.
Latexmk: Errors, so I did not complete making targets
Collected error summary (may duplicate other messages):
  pdflatex: Command for 'pdflatex' gave return code 1
      Refer to 'perpare.log' and/or above output for details

Latexmk: If appropriate, the -f option can be used to get latexmk
  to try to force complete processing.
C:\texlive\2023\bin\windows\runscript.tlu:921: command failed with exit code 12:
perl.exe c:\texlive\2023\texmf-dist\scripts\latexmk\latexmk.pl -synctex=1 -interaction=nonstopmode -file-line-error -pdf -outdir=d:/Documents/Math-master/advanced-math/knowledge/0-perpare d:/Documents/Math-master/advanced-math/knowledge/0-perpare/perpare

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