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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "L:=(2*pi*sigma^2)^(-
n/2)*exp((sum((x[i]-mu)^2,i=1..n)/(2*sigma^2)));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"LG*&),$*&%#piG\"\"\")%&sigmaG\"\"#F*F-,$%\"nG#!\"\"
F-F*-%$expG6#,$*&,&*&F/F*)%#muGF-F*F*-%$sumG6$,&*$)&%\"xG6#%\"iGF-F*F*
*(F-F*FAF*F:F*F1/FD;F*F/F*F*F,!\"##F*F-F*" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 24 "In omega 0, mu=sigma^2=t" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "subs(\{mu=t,sigma^2=t\},%);" }}{PARA 8 "" 1 "" {TEXT 
-1 61 "Error, wrong number (or type) of parameters in function subs\n
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "diff(%,t);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#,&**),$*&%#piG\"\"\"%\"tGF)\"\"#,$%\"nG#!\"\"F+
F)F-F)F*F/-%$expG6#,$*&,&*&F-F))F*F+F)F)-%$sumG6$,&*$)&%\"xG6#%\"iGF+F
)F)*(F+F)F>F)F*F)F//FA;F)F-F)F)%&sigmaG!\"##F)F+F)F.*,FGF)F%F),&*&F-F)
F*F)F+-F96$,$F>FFFCF)F)FEFFF0F)F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "theta:=solve(%=0,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%&thetaG6$,$*&%\"nG!\"\",&-%$sumG6$&%\"xG6#%\"iG/F1;\"\"\"F(\"\"#*
&F5F4-%%sqrtG6#,&*$)F+F5F4F4*(F5F4)F(F5F4)%&sigmaGF5F4F4F4F4F4#F4\"\"%
,$*&F(F),&F+F5*&F5F4F7F4F)F4FA" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "so this is my estimato
r for theta, which gives the following L*0" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 36 "Los:=subs(mu=theta,sigma^2=theta,L);" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#>%$LosG*&),$*&%#piG\"\"\"6$,$*&%\"nG!\"\",&-%$su
mG6$&%\"xG6#%\"iG/F7;F*F.\"\"#*&F:F*-%%sqrtG6#,&*$)F1F:F*F**(F:F*)F.F:
F*)%&sigmaGF:F*F*F*F*F*#F*\"\"%,$*&F.F/,&F1F:*&F:F*F<F*F/F*FFF*F:,$F.#
F/F:F*-%$expG6#,$*&,&*&F.F*)6$,$*&F.F/,&F1F:*&F:F*-F=6#,&F@F**(F:F*FCF
*F+F*F*F*F*F*FF,$*&F.F/,&F1F:*&F:F*FenF*F/F*FFF:F*F*-F26$,&*$)F4F:F*F*
*(F:F*F4F*FVF*F/F8F*F*FE!\"##F*F:F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 66 "In omega, L star has already been determined., where y=mean of \+
x's" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "Ls:=(2*pi*sum((x[i]-
y)^2,i=1..n))^(-n/2)*exp(-n/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#
LsG*&),$*&%#piG\"\"\",&*&%\"nGF*)%\"yG\"\"#F*F*-%$sumG6$,&*$)&%\"xG6#%
\"iGF0F*F**(F0F*F7F*F/F*!\"\"/F:;F*F-F*F*F0,$F-#F<F0F*-%$expG6#F?F*" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "with that done, we can move on t
o lambda." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "lambda:=Los/Ls
;" }}{PARA 8 "" 1 "" {TEXT -1 102 "Error, (in convert/hypergeom) Summa
nd is singular at local_i = local_i+1 in the interval of summation\n" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "f:=(2*pi*y)^(-n/2)*exp(su
m((x[i]-y)^2,i=1..n)/(2*y));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG
*&),$*&%#piG\"\"\"%\"yGF*\"\"#,$%\"nG#!\"\"F,F*-%$expG6#,$*&,&*&F.F*)F
+F,F*F*-%$sumG6$,&*$)&%\"xG6#%\"iGF,F*F**(F,F*F?F*F+F*F0/FB;F*F.F*F*F+
F0#F*F,F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "yhat:=solve(di
ff(f,y)=0,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%yhatG6$,$*&%\"nG!
\"\",&F(\"\"\"*$-%%sqrtG6#,&*$)F(\"\"#F+F+*(\"\"%F+F(F+-%$sumG6$*$)&%
\"xG6#%\"iGF3F+/F>;F+F(F+F+F+F+F+#F+F3,$*&F(F),&F(F+F,F)F+FA" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "los:=subs(y=yhat,f);" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$losG*&),$*&%#piG\"\"\"6$,$*&%\"nG!
\"\",&F.F**$-%%sqrtG6#,&*$)F.\"\"#F*F**(\"\"%F*F.F*-%$sumG6$*$)&%\"xG6
#%\"iGF8F*/FC;F*F.F*F*F*F*F*#F*F8,$*&F.F/,&F.F*F1F/F*FFF*F8,$F.#F/F8F*
-%$expG6#,$*&,&*&F.F*)F+F8F*F*-F<6$,&F>F**(F8F*F@F*F+F*F/FDF*F*F+F/FFF
*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "lambda:=los/ls;" }}
{PARA 8 "" 1 "" {TEXT -1 102 "Error, (in convert/hypergeom) Summand is
 singular at local_i = local_i+1 in the interval of summation\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "15 0 0" 15 }
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