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"int(f3,x=-1..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "Or, we could even do this (getting the same, correct answer - why?):" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "int(f3,x=-infinity..infinity);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "int(f3,x=-1..-0.5);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#$\"+6_@@$)!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "The correspond ing mean is:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "int(x*f3,x=-1..1.0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+[G' Rk'!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "\"Q3\":" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "median:=solve(F=1/2,x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%'medianG,&\"\"\"F&*$-%%sqrtG6#\"\"#F &!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 57 "Note that now we have o btained a single (correct) answer." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "sigma:=1/2/eval(f,x=median)/sqrt(13 71);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&sigmaG,$*&-%%sqrtG6#\"\"#\" \"\"-F(6#\"%r8F+#F+\"%UF" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "The a pproximate (Normal) pdf of the sample median:" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "fm:=1/sqrt(2*Pi)/sigma*exp(- (x-median)^2/2/sigma^2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "plot(fm,x=-1..1);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7gp7$$!\"\"\"\"!$\"3wDg!Q:'H65!$?#7$$!3ommm ;p0k&*!#=$\"3#)o@s7\"49#>!$\">7$$!3wKL$36_;G!$V\"7$$!3:mmm\"4m(G$)F1$\"3s&)y%e**yP.* !$@\"7$$!3\"QLL3i.9!zF1$\"3)3.3\"*QCg\\\"!$+\"7$$!3\"ommT!R=0vF1$\"3!R hvZeo\")\\*!#%)7$$!3u****\\P8#\\4(F1$\"3q*z(y_]qXD!#o7$$!3+nm;/siqmF1$ \"3+hG)yIqRe]!#L7$$!3hmmm\">s%HaF1$\"3!eYAoNeW$G!#E7$$!3]LL$3x&y8_F1$ \"3FIbD?(QO.$!#B7$$!3Q+++]$*4)*\\F1$\"3'GY(*[H0s1*!#@7$$!3j++]Pj&R%\\F 1$\"3ZS%[x)=)Q5$!#?7$$!3K+++DL\")*)[F1$\"3RZT'*>tb/)*F\\q7$$!3,++]7.nN 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$!3G]P%[J6'eMF1$\"3cxJFBsQ_MFgq7$$!3!*\\i8x=F\\q7$$!3 !QLL$eW%o7$F1$\"3g^v;]Q`@:!#A7$$!3*RLLLtIf$HF1$\"3YbXo\\:uRX!#D7$$!3]+ +]PYx\"\\#F1$\"3GDQw_O1b!#m 7$$!3)3LLL3x%z#)Fgq$\"3NO1'eiK:K)!##)7$$!3KMLL3s$QM%Fgq$\"3c!pJooE(>H! #)*7$$!3]^omm;zr)*Ffp$\"3#Q'fVxBta1\"!$;#7$$\"3#z ****\\_qn2#F1$\"3Q%oiem-]5\"!$Y#7$$\"3U)***\\i&p@[#F1$\"3Y5gY([D?5\"!$ x#7$$\"3B)****\\2'HKHF1$\"3RB\"o#)[Kp7#!$9$7$$\"3ElmmmZvOLF1$F*F*7$$\" 3i******\\2goPF1Fjdl7$$\"3UKL$eR<*fTF1Fjdl7$$\"3m******\\)Hxe%F1Fjdl7$ $\"3ckm;H!o-*\\F1Fjdl7$$\"3y)***\\7k.6aF1Fjdl7$$\"3#emmmT9C#eF1Fjdl7$$ \"33****\\i!*3`iF1Fjdl7$$\"3%QLLL$*zym'F1Fjdl7$$\"3wKLL3N1#4(F1Fjdl7$$ \"3Nmm;HYt7vF1Fjdl7$$\"3Y*******p(G**yF1Fjdl7$$\"3]mmmT6KU$)F1Fjdl7$$ \"3fKLLLbdQ()F1Fjdl7$$\"3[++]i`1h\"*F1Fjdl7$$\"3W++]P?Wl&*F1Fjdl7$$\" \"\"F*Fjdl-%'COLOURG6&%$RGBG$\"#5F)FjdlFjdl-%+AXESLABELSG6$Q\"x6\"Q!Fe hl-%%VIEWG6$;F(Figl%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "The probability of being bigger than -0.4 is then computed by:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "int(fm ,x=-0.4..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+aQ`$G#!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "int(fm,x=-0.4..1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+aQ`$G#!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "Note that the two answers are identical (the plot expl ains why)." }{MPLTEXT 1 0 0 "" }}}}{MARK "28 0 0" 64 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }