{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 23 "Courier" 1 10 0 0 0 0 0 0 0 0 0 0 3 0 0 1 }{CSTYLE " " -1 35 "" 0 1 104 64 92 1 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 256 "" 1 14 0 0 0 0 1 2 2 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE " Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Times " 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1 0 2 2 15 2 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 22 "Cviceni ze statistiky\n" }{TEXT 256 23 "priklady Marie Budikove" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "with(Statistics);\nwith(stats);\nwith(RealDomain);" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#7ds%2AbsoluteDeviationG%*AreaChartG%) BarChartG%*BootstrapG%(BoxPlotG%+BubblePlotG%$CDFG%$CGFG%.CentralMomen tG%7CharacteristicFunctionG%;ChiSquareGoodnessOfFitTestG%:ChiSquareInd ependenceTestG%;ChiSquareSuitableModelTestG%,ColumnGraphG%,Correlation G%2CorrelationMatrixG%&CountG%-CountMissingG%+CovarianceG%1CovarianceM atrixG%)CumulantG%;CumulantGeneratingFunctionG%?CumulativeDistribution FunctionG%2CumulativeProductG%.CumulativeSumG%3CumulativeSumChartG%,Da taSummaryG%'DecileG%,DensityPlotG%+DiscretizeG%-DistributionG%*ErrorPl otG%0EvaluateToFloatG%.ExpectedValueG%/ExponentialFitG%5ExponentialSmo othingG%,FailureRateG%2FisherInformationG%$FitG%1FivePointSummaryG%.Fr equencyPlotG%/FrequencyTableG%.GeometricMeanG%-HarmonicMeanG%+HazardRa teG%*HistogramG%,InformationG%8InteractiveDataAnalysisG%3Interquartile RangeG%8InverseSurvivalFunctionG%%JoinG%.KernelDensityG%2KernelDensity PlotG%4KernelDensitySampleG%)KurtosisG%+LikelihoodG%9LikelihoodRatioSt atisticG%*LineChartG%-LinearFilterG%*LinearFitG%.LogLikelihoodG%/Logar ithmicFitG%$MGFG%$MLEG%.MakeProcedureG%:MaximumLikelihoodEstimateG%%Me anG%.MeanDeviationG%'MedianG%0MedianDeviationG%+MillsRatioG%%ModeG%'Mo mentG%9MomentGeneratingFunctionG%.MovingAverageG%-MovingMedianG%0Movin gStatisticG%-NonlinearFitG%+NormalPlotG%7OneSampleChiSquareTestG%/OneS ampleTTestG%/OneSampleZTestG%,OneWayANOVAG%,OrderByRankG%/OrderStatist icG%$PDFG%+PercentileG%)PieChartG%*PointPlotG%.PolynomialFitG%)PowerFi tG%,ProbabilityG%;ProbabilityDensityFunctionG%4ProbabilityFunctionG%0P robabilityPlotG%2ProfileLikelihoodG%5ProfileLogLikelihoodG%.QuadraticM eanG%)QuantileG%-QuantilePlotG%)QuartileG%/RandomVariableG%&RangeG%%Ra nkG%'RemoveG%.RemoveInRangeG%1RemoveNonNumericG%'SampleG%,ScatterPlotG %&ScoreG%'SelectG%.SelectInRangeG%1SelectNonNumericG%1ShapiroWilkWTest G%(ShuffleG%)SkewnessG%%SortG%2StandardDeviationG%.StandardErrorG%3Sta ndardizedMomentG%(SupportG%,SurfacePlotG%1SurvivalFunctionG%&TallyG%*T allyIntoG%%TrimG%,TrimmedMeanG%/TwoSampleFTestG%5TwoSamplePairedTTestG %/TwoSampleTTestG%/TwoSampleZTestG%)VarianceG%*VariationG%6WeightedMov ingAverageG%*WinsorizeG%/WinsorizedMeanG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7*%&anovaG%)describeG%$fitG%+importdataG%'randomG%*statevalfG%*s tatplotsG%*transformG" }}{PARA 7 "" 1 "" {TEXT -1 318 "Warning, these \+ protected names have been redefined and unprotected: Im, Re, ^, arccos , arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin, \+ arcsinh, arctan, arctanh, cos, cosh, cot, coth, csc, csch, eval, exp, \+ expand, limit, ln, log, sec, sech, signum, simplify, sin, sinh, solve, sqrt, surd, tan, tanh\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7H%#ImG%#R eG%\"^G%'arccosG%(arccoshG%'arccotG%(arccothG%'arccscG%(arccschG%'arcs ecG%(arcsechG%'arcsinG%(arcsinhG%'arctanG%(arctanhG%$cosG%%coshG%$cotG %%cothG%$cscG%%cschG%%evalG%$expG%'expandG%&limitG%#lnG%$logG%$secG%%s echG%'signumG%)simplifyG%$sinG%%sinhG%&solveG%%sqrtG%%surdG%$tanG%%tan hG" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 1 "1" }}{EXCHG {PARA 15 "" 0 " " {TEXT -1 4 "The " }{TEXT 35 18 "normald[mu, sigma]" }{TEXT -1 51 " d istribution has the probability density function " }}{PARA 0 "" 0 "" {TEXT 23 53 " exp( -(x-mu)^2/2/sigma^2 ) / sqrt(2*Pi*sigma^2)" }} {PARA 14 "" 0 "" {TEXT -1 14 "The parameter " }{TEXT 35 2 "mu" }{TEXT -1 23 " has the default value " }{TEXT 35 1 "0" }{TEXT -1 19 " and the parameter " }{TEXT 35 5 "sigma" }{TEXT -1 23 " has the default value \+ " }{TEXT 35 1 "1" }{TEXT -1 12 ". Note that " }{TEXT 35 5 "sigma" } {TEXT -1 61 " is the standard deviation and not the variance. Constrai nt: " }{TEXT 35 5 "sigma" }{TEXT -1 19 " must be positive. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 10 "Prikla d 1." }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Dok\341zat p\370epo\350tov \375 vzorec " }{XPPEDIT 18 0 "Phi(-u) = 1-Phi(u);" "6#/-%$PhiG6#,$%\"u G!\"\",&\"\"\"F+-F%6#F(F)" }{TEXT -1 1 "." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "X := RandomV ariable(Normal(0, sqrt(1)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG %#_RG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "phi:=ProbabilityDe nsityFunction(X,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$phiG,$*&#\" \"\"\"\"#F(*(F)F'%#PiG#!\"\"F)-%$expG6#,$*&F)F-%\"tGF)F-F(F(F(" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "distribu\350n\355 funkce:" } {MPLTEXT 1 0 30 "\nPhi:=int(phi,t=-infinity..x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$PhiG,&#\"\"\"\"\"#F'*&F&F'-%$erfG6#,$*(F(!\"\"F(F&% \"xGF'F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "plot(\{subs (t=x,phi),Phi\},x=-10..10,title=\"Hustota a distrib. f. N(0,1)\");" }} {PARA 13 "" 1 "" {GLPLOT2D 447 447 447 {PLOTDATA 2 "6'-%'CURVESG6$7io7 $$!#5\"\"!$\"37@kqE')f%p(!#S7$$!3!pmmm\"p0k&*!#<$\"3K(QS%yAhsa!#Q7$$!3 uKL$3j\">!#O7$$!3WmmmT%p\"e()F1$\"3L7nt&\\M!#L7$$!3OLL$3i.9!zF1$\"3AAvmxrX16!#J7$$! 3fmm;/R=0vF1$\"33(f(y#og9M#!#I7$$!3k++]P8#\\4(F1$\"39,RgU[?zY!#H7$$!3K mm;/siqmF1$\"3%frY5QJ'y')!#G7$$!3Q****\\(y$pZiF1$\"3?=#G^AvIL\"!#E7$$! 3jKLL$yaE\"eF1$\"3H!*>T3*Rs$=!#D7$$!3s%HaF1$\"3m)>/Xp(R$e\"!#C7 $$!3]******\\$*4)*\\F1$\"3cNuD=G\"4]\"!#B7$$!3o******\\_&\\c%F1$\"3I#f ovYW2>\"!#A7$$!3%)******\\1aZTF1$\"3.<*3,iuqL(Ffp7$$!3Imm;/#)[oPF1$\"3 K94r^!>#*G$!#@7$$!3%HLLL=exJ$F1$\"3^44!QpnUi\"!#?7$$!3!GLL$eW%o7$F1$\" 3Hf&e4%H)[+$Fgq7$$!3lKLLL2$f$HF1$\"3kJc+0O/g`Fgq7$$!3CmmT&o_Qr#F1$\"3x P9tJ/u.5!#>7$$!3%)****\\PYx\"\\#F1$\"3k\\#\\#Go=*y\"Fgr7$$!3smmTNz>&H# F1$\"3C)[*Gl18kGFgr7$$!3gLLLL7i)4#F1$\"3MU&fS\"*36T%Fgr7$$!39mmTNa%H)= F1$\"3MO;%4b(pwnFgr7$$!3o)***\\P'psm\"F1$\"3u>'*RD,sP**Fgr7$$!3#))**\\ iX#ek:F1$\"3oN4OAT9t6!#=7$$!3%*)****\\F&*=Y\"F1$\"3E6%=Dtl.P\"Fft7$$!3 1***\\P43#f8F1$\"3WzH8%R_Re\"Fft7$$!3?****\\74_c7F1$\"3Q_/&\\'[i6=Fft7 $$!3GK$e9hx$\\6F1$\"3egY(zzO31#Fft7$$!3PlmT5VBU5F1$\"3\")=Nc$osvJ#Fft7 $$!3]%)*\\P454N*Fft$\"3U9!3#*)RawDFft7$$!3M:LL$3x%z#)Fft$\"3%**HCVQe<$ GFft7$$!3'*=Le9rc&H(Fft$\"3[!R*>sHEdIFft7$$!3gAL$e9d;J'Fft$\"3=J:)e'f# *oKFft7$$!3BEL3xruF`Fft$\"3'G$z'y`p:Y$Fft7$$!3()HLL3s$QM%Fft$\"3w!Q*yy :DIOFft7$$!3>****\\ivF@AFft$\"3IEdR!Q1A*QFft7$$!3]^omm;zr)*Fgq$\"3EHYf >%G#*)RFft7$$\"3aPL$3-Dg5#Fft$\"3F(RwMMC>!RFft7$$\"3fVLLezw5VFft$\"3I \\6=6-XNOFft7$$\"3W3+]ibQq_Fft$\"3Mp+7Ou5sMFft7$$\"3JtmmmJ+IiFft$\"3yT $*zUqq&G$Fft7$$\"3=QL$3x?'*=(Fft$\"3c*Q*R\"R733$Fft7$$\"3-.++v$Q#\\\") Fft$\"3[#Hs3%f@iGFft7$$\"3iRL3x;l&=*Fft$\"3Cf&Gap6jh#Fft7$$\"3inm\"z\\ 1A-\"F1$\"3uII2/G)fO#Fft7$$\"3G,]7Gy%e7\"F1$\"3\"yIKpwXn6#Fft7$$\"3%\\ LL$e\"*[H7F1$\"3wov1t2`t=Fft7$$\"3D,+v$zglL\"F1$\"3Qs/(=f\\Ij\"Fft7$$ \"3cnm;HCjV9F1$\"3,Po1V.@29Fft7$$\"3)QL$ekSq]:F1$\"3+'\\`ew!y)>\"Fft7$ $\"3=++++dxd;F1$\"3pbohS?e45Fft7$$\"3Q++]7JFn=F1$\"3?,mm?;!)ypFgr7$$\" 3e+++D0xw?F1$\"3R(Hmxa$*ph%Fgr7$$\"3%3+]P/q%zAF1$\"3WN0n(RV!pHFgr7$$\" 35,+]i&p@[#F1$\"3a3i-#oSC$=Fgr7$$\"3b++v=GB2FF1$\"3l(3fe`8>-\"Fgr7$$\" 3++++vgHKHF1$\"3<$*y2y;^p\"y2c\"F`p7$$\"3X,+]7k.6aF1$\"3Wn+xjmz\\ \\`QiW5!#M7$$\"3[++]i`1h\"*F1$\"3!3%es!H.o\"Ffp7$F]q$\"3u\\pqYA'>@) Ffp7$Fcq$\"3o)oyxR]r`%Faq7$F^r$\"3%e>*)p%Gui;Fgq7$Fcr$\"3K:L(4n'GDLFgq 7$Fir$\"3S#>!)\\*GLbjFgq7$F^s$\"3g4j9t\"*3'3\"Fgr7$Fcs$\"3#*G:x`^^#z\" Fgr7$Fhs$\"3ehntY\")Q&)HFgr7$F]t$\"3Q!4[#f+/tZFgr7$Fht$\"3gTyF*\\&\\)= (Fgr7$Fbu$\"3I87_VejW5Fft7$F\\v$\"3y*Q4qH:l[\"Fft7$Ffv$\"3lbRjt0]Q?Fft 7$F`w$\"3AJ;:&)3mREFft7$Fjw$\"3$pbNg3\\+K$Fft7$F_x$\"3m*46f:s57%Fft7$F dx$\"3u&eb)))yhg\\Fft7$Fix$\"3CxlQ,F,MeFft7$F^y$\"3QC0iRt$zm'Fft7$Fhy$ \"3IdPFJ%yNL(Fft7$Fbz$\"3&*f'HGY?W#zFft7$F\\[l$\"3'3xO+7%em%)Fft7$Ff[l $\"32Bqp)pdb!*)Fft7$F`\\l$\"3%>@U5,)yb#*Fft7$Fj\\l$\"3BY)))4E'=8&*Fft7 $F_]l$\"3m8W94Fo!p*Fft7$Fd]l$\"3A!))z1G')3\")*Fft7$Fi]l$\"3MeS&fx*****Fft7$Ff`l$\"2U^@_)p******F17$F[al$\" 2/'[p'o*******F17$F`al$\"2yC)*4(********F17$Feal$\"2s$z)z*********F17$ Fjal$\"2sBq)**********F17$F_bl$\"2UR$************F17$Fdbl$\"2-r******* ******F17$Fibl$\"2m)**************F17$F^cl$\"\"\"F*7$FcclFf_m7$FiclFf_ m7$F^dlFf_m7$FcdlFf_m-Ffdl6&FhdlF[elFidlF[el-%+AXESLABELSG6$Q\"x6\"Q!F b`m-%&TITLEG6#Q=Hustota~a~distrib.~f.~N(0,1)Fb`m-%%VIEWG6$;F(Fcdl%(DEF AULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve \+ 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Phi:=unappl y(Phi,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$PhiGf*6#%\"xG6\"6$%)op eratorG%&arrowGF(,&#\"\"\"\"\"#F.*&F-F.-%$erfG6#,$*&F-F.*&F/F-9$F.F.F. F.F.F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Reseni prikladu 1: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "Phi(-x)+Phi(x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 10 "priklad 2." }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 104 "Jak\341 je pravd\354podobnost, \236e n\341hodn\341 \+ veli\350ina X ~ N(20,16) nabude hodnotu\nmen\232\355 ne\236 12 nebo v \354t\232\355 ne\236 28?" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 6 "resen i" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Oznacme zminenou nhodnou veli cinu X" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "X := RandomVariab le(Normal(20, sqrt(16)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG%#_ RG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 95 "Hledanou pravdepodobnost vy pocitame pomoci pravdepodobnosti komplementarniho jevu, bude presne:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "1-Probability(\{X > 12 , \+ X<28\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\"\"F$-%$erfG6#*$\"\"# #F$F)!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "kde" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 " erf(x) = 2/sqrt(Pi) * Int(exp(-t^2 ), t=0..x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$erfG6#%\"xG,$,$-%$I ntG6$-%$expG6#,$*$)%\"tG\"\"#\"\"\"!\"\"/F3;\"\"!F'*&F4F5%#PiG#F6F4F5 " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "je " }{HYPERLNK 17 "the error \+ function (chybova funkce)" 2 "erf" "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 15 "nebo numericky:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "1 -Probability(\{X > 12 , X<28\},'numeric');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*QE+b%!#5" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 " Priklad 3" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 176 " Dlouhodobe zku.enos ti s vysledky testu z matematiky na st.edni .kole oprav.uji\nu.itele k tomu, aby po.et bod. v testu dosa.enych pova.oval za nahodnou veli.in u X\ns rozlozenim " }{XPPEDIT 18 0 "N(mu, sigma^2);" "6#-%\"NG6$%#muG* $%&sigmaG\"\"#" }{TEXT -1 74 ". Ucitel se rozhodl, ze bude test znamko vat podle nasledujicich pravidel:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "unassign('sigma','mu','i','X');\nZn:=piecewise(\nX>m u+sigma,1,\nX>mu,2,\nX>mu-sigma,3,\nX>mu-2*sigma,4,5);\nZN:=unapply(Zn ,X);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ZnG-%*PIECEWISEG6'7$\"\"\"2 ,&%#muGF)%&sigmaGF)%\"XG7$\"\"#2F,F.7$\"\"$2,&F,F)F-!\"\"F.7$\"\"%2,&F ,F)*&F0F)F-F)F6F.7$\"\"&%*otherwiseG" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%#ZNGf*6#%\"XG6\"6$%)operatorG%&arrowGF(-%*piecewiseG6+2,&%#muG\"\" \"%&sigmaGF29$F22F1F4\"\"#2,&F1F2F3!\"\"F4\"\"$2,&F1F2*&F6F2F3F2F9F4\" \"%\"\"&F(F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 116 "Jak\341 je pra vdepodobnost, \236e n\341hodne vybran\375 student ze skupiny zkou\232e n\375ch studentu bude ohodnocen vybranou zn\341mkou?" }{MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "Cond: =i->#`if`(i=1,\nop(2*i-1,Zn)#,\{op(2*i-1,Zn), not(op(2*i-3,Zn))\})\n; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%CondGf*6#%\"iG6\"6$%)operatorG% &arrowGF(-%#opG6$,&*&\"\"#\"\"\"9$F2F2F2!\"\"%#ZnGF(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Cond(1);Cond(2);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#2,&%#muG\"\"\"%&sigmaGF&%\"XG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#2%#muG%\"XG" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 6 "res eni" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "with(RealDomain):\nwi th(Statistics):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "X := Ran domVariable(Normal(mu,sigma));\nCond(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG%$_R2G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#2,&%#muG\"\"\"%& sigmaGF&%$_R2G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 190 "p[0]:=0; \nassume(sigma>0);\nfor i from 1 to (nops(Zn)-1)/2 do\nprintf(`Pravde podobnost znamky %a, je`,op(2*i,Zn)); \nprint(Cond(i)); #podminka\np[i ]:=simplify(Probability(\{Cond(i)\}),'numeric');\n" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 78 "q[i]:=evalf(p[i]-p[i-1]):\nprintf(%f,q[i]);\nprint( `______________________`)\nod;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"pG6#\"\"!F'" }}{PARA 6 "" 1 "" {TEXT -1 28 "Pravdepodobnost znamky 1, je" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#2,&%#muG\"\"\"%'sigma|irGF&%$_R2G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"pG6#\"\"\",&#F'\"\"#F'*&#F'F*F'-%$erfG6#,$*&F*!\" \"F*F)F'F'F2" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"qG6#\"\"\"$\"+SDb 'e\"!#5" }}{PARA 6 "" 1 "" {TEXT -1 8 "0.158655" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%7______________________G" }}{PARA 6 "" 1 "" {TEXT -1 28 "Pravdepodobnost znamky 2, je" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#2% #muG%$_R2G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"pG6#\"\"##\"\"\"F' " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"qG6#\"\"#$\"+guW8M!#5" }} {PARA 6 "" 1 "" {TEXT -1 8 "0.341345" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#%7______________________G" }}{PARA 6 "" 1 "" {TEXT -1 28 "Pravdepodo bnost znamky 3, je" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#2,&%#muG\"\"\"%' sigma|irG!\"\"%$_R2G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"pG6#\"\"$ ,&#\"\"\"\"\"#F**&F)F*-%$erfG6#,$*&F+!\"\"F+F)F*F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"qG6#\"\"$$\"+guW8M!#5" }}{PARA 6 "" 1 "" {TEXT -1 8 "0.341345" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%7__________________ ____G" }}{PARA 6 "" 1 "" {TEXT -1 28 "Pravdepodobnost znamky 4, je" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#2,&%#muG\"\"\"*&\"\"#F&%'sigma|irGF&! \"\"%$_R2G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"pG6#\"\"%,&#\"\"\" \"\"#F**&F)F*-%$erfG6#*$F+F)F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>& %\"qG6#\"\"%$\"+?70f8!#5" }}{PARA 6 "" 1 "" {TEXT -1 8 "0.135905" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%7______________________G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "Density Plot(RandomVariable(Normal(2,1)),range = -1..4, thickness = 3,xtickmar ks=[0,1,2,3]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 982 268 268 {PLOTDATA 2 "6'-%'CURVESG6$7W7$$!\"\"\"\"!$\" 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"6#>%\"fGf*6#%\"tG6\"6$%)operatorG%&arrowGF(-_%+Sta tisticsG%)QuantileG6%%\"XG9$%(numericGF(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 7 "" 1 "" {TEXT -1 114 "Warning, numeri c quantile computation failed to converge; consider increasing _EnvSta tisticsIterations or Digits.\n" }}{PARA 7 "" 1 "" {TEXT -1 113 "Warnin g, numeric quantile computation from CDF failed to converge; consider \+ increasing _EnvStatisticsIterations.\n" }}{PARA 7 "" 1 "" {TEXT -1 114 "Warning, numeric quantile computation failed to converge; conside r increasing _EnvStatisticsIterations or Digits.\n" }}{PARA 7 "" 1 "" {TEXT -1 113 "Warning, numeric quantile computation from CDF failed to converge; consider increasing _EnvStatisticsIterations.\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 388 "t:='t';\nprint(`\\n`);\nfor i from 1 to 85 do\nprintf(`_`);\nod;\nprint(`\\n`);\n\nprintf(` \+ Tabulka Kvantilu`);\n\nprintf(` %a`,ProbabilityDe nsityFunction(X, 't'));\nT:=``:\nfor j from 0.1 by 0.1 to .9 do\n K: =5;\n for t from 0 to K-1 do\n printf(`| %0.3f |%+2.7f |`,(t+j) /K,f((t+j)/K));\n od:\nprintf(`|\\n`);\nod:\n\nprint(`\\n`);\nfor i \+ from 1 to 85 do\nprintf(`_`);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"tGF$" }}{PARA 12 "" 1 " " {XPPMATH 20 "6#%\"|+G" }}{PARA 6 "" 1 "" {TEXT -1 85 "______________ ______________________________________________________________________ _" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#%\"|+G" }}{PARA 6 "" 1 "" {TEXT -1 37 " Tabulka Kvantilu" }}{PARA 6 "" 1 "" {TEXT -1 48 " 1/2*2^(1/2)/Pi^(1/2)*exp(-1/2*t^2)" }}{PARA 6 "" 1 "" {TEXT -1 106 "| 0.020 |-2.0537489 || 0.220 |-0.7721932 || 0.420 | -0.2018935 || 0.620 |+0.3054808 || 0.820 |+0.9153651 ||" }}{PARA 6 "" 1 "" {TEXT -1 106 "| 0.040 |-1.7506861 || 0.240 |-0.7063026 || 0.440 | -0.1509692 || 0.640 |+0.3584588 || 0.840 |+0.9944579 ||" }}{PARA 6 "" 1 "" {TEXT -1 106 "| 0.060 |-1.5547736 || 0.260 |-0.6433454 || 0.460 | -0.1004337 || 0.660 |+0.4124631 || 0.860 |+1.0803193 ||" }}{PARA 6 "" 1 "" {TEXT -1 106 "| 0.080 |-1.4050716 || 0.280 |-0.5828415 || 0.480 | -0.0501536 || 0.680 |+0.4676988 || 0.880 |+1.1749868 ||" }}{PARA 6 "" 1 "" {TEXT -1 106 "| 0.100 |-1.2815516 || 0.300 |-0.5244005 || 0.500 | +0.0000000 || 0.700 |+0.5244005 || 0.900 |+1.2815516 ||" }}{PARA 6 "" 1 "" {TEXT -1 106 "| 0.120 |-1.1749868 || 0.320 |-0.4676988 || 0.520 | +0.0501536 || 0.720 |+0.5828415 || 0.920 |+1.4050716 ||" }}{PARA 6 "" 1 "" {TEXT -1 106 "| 0.140 |-1.0803193 || 0.340 |-0.4124631 || 0.540 | +0.1004337 || 0.740 |+0.6433454 || 0.940 |+1.5547736 ||" }}{PARA 6 "" 1 "" {TEXT -1 106 "| 0.160 |-0.9944579 || 0.360 |-0.3584588 || 0.560 | +0.1509692 || 0.760 |+0.7063026 || 0.960 |+1.7506861 ||" }}{PARA 6 "" 1 "" {TEXT -1 106 "| 0.180 |-0.9153651 || 0.380 |-0.3054808 || 0.580 | +0.2018935 || 0.780 |+0.7721932 || 0.980 |+2.0537489 ||" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#%\"|+G" }}{PARA 6 "" 1 "" {TEXT 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"6#>&%\"XG6#\"\"%%&_R530G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"tGF$" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"ZG%&_R531G" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#,$*,\"\"#\"\"\"\"\"$!\"\"F'#F&F%%#PiGF(,&F&F&*&F'F(%\"tGF%F&!\"#F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "sice" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "Y:= (X[1]*sqrt(3)/sqrt(sum(X[i]^2,i = 2 .. 4)));\nsim plify(PDF(Y, t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"YG*(%&_R527G \"\"\"\"\"$#F'\"\"#,(*$)%&_R528GF*F'F'*$)%&_R529GF*F'F'*$)%&_R530GF*F' F'#!\"\"F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%FAILG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "ale" }{MPLTEXT 1 0 36 "\nY:= (sqrt(sum(X[i ]^2,i = 2 .. 4)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"YG*$,(*$)%&_ R528G\"\"#\"\"\"F+*$)%&_R529GF*F+F+*$)%&_R530GF*F+F+#F+F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "simplify(PDF(Y,t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*PIECEW ISEG6$7$\"\"!1%\"tGF'7$**F)\"\"#F,#\"\"\"F,-%$expG6#,$*&F,!\"\"F)F,F4F .%#PiG#F4F,2F'F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "nu:=3; \nCh:=RandomVariable(ChiSquare(nu));\nsimplify(PDF(Ch, t));" }}{PARA 0 "" 0 "" {TEXT -1 5 " " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#nuG \"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ChG%&_R533G" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#-%*PIECEWISEG6$7$\"\"!2%\"tGF'7$,$*&#\"\"\"\"\"# F.**F/F-%#PiG#!\"\"F/F)F--%$expG6#,$*&F/F3F)F.F3F.F.F.1F'F)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "A:= (X[1]*sqrt(3)/sqrt(Ch)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG*(%%_R38G\"\"\"\"\"$#F'\"\"# %%_R50G#!\"\"F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "simplify (PDF(A, t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"\"'\"\"\"\"\"$#F &\"\"#%#PiG!\"\",(*$)%\"tG\"\"%F&F&*&F%F&)F/F)F&F&\"\"*F&F+F&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "nu:=3;\nCh:=RandomVariable(S tudentT(3));\nsimplify(PDF(Ch, t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%#nuG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ChG%%_R51G" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,$**\"\"'\"\"\"\"\"$#F&\"\"#%#PiG!\"\" ,&F'F&*$)%\"tGF)F&F&!\"#F&" }}}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 9 "P riklad 8" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 96 "Nech\235 n\341hodn\341 veli\350ina X ~ F(n1, n2). Jak\351 rozlo\236en\355 m\341 transformova n\341 n\341hodn\341\nveli\350ina Y = 1/X?" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Fisher f-distribution:" }}}{EXCHG {PARA 15 "" 0 "" {TEXT -1 110 "The f-ratio distribution is a continuous probability distribut ion with probability density function given by: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 150 "f(t) = piecewise(t < 0,0,GAMMA(1/2*nu+1/2*omega)*(nu /omega)^(1/2*nu)*t^(1/2*nu-1)/GAMMA(1/2*nu)/GAMMA(1/2*omega)/((1+nu/om ega*t)^(1/2*nu+1/2*omega)));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"fG6#%\"tG-%*PIECEWISEG6$7$\"\"!2F 'F,7$*.-%&GAMMAG6#,&*&\"\"#!\"\"%#nuG\"\"\"F8*&F5F6%&omegaGF8F8F8)*&F7 F8F:F6,$*&F5F6F7F8F8F8)F',&*&F5F6F7F8F8F8F6F8-F16#F=F6-F16#,$*&F5F6F:F 8F8F6),&F8F8*(F7F8F:F6F'F8F8F3F6%*otherwiseG" }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "nu:='nu'; \nX := RandomVariable(FRatio(nu,omega)):\nA:=simplify(PDF(X, u));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#nuGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%*PIECEWISEG6$7$\"\"!2%\"uGF)7$*.-%&GAMMAG6#,&*&\"\"#!\" \"%#nuG\"\"\"F6*&F3F4%&omegaGF6F6F6)*&F5F6F8F4,$*&F3F4F5F6F6F6)F+,&*&F 3F4F5F6F6F6F4F6-F/6#F;F4-F/6#,$*&F3F4F8F6F6F4)*&,&F8F6*&F5F6F+F6F6F6F8 F4,&*&F3F4F5F6F4*&F3F4F8F6F4F61F)F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "B:=simplify(PDF(1/X, u));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG-%*PIECEWISEG6$7$\"\"!1%\"uGF)7$*.)F+,&*&\"\"#!\" \"%&omegaG\"\"\"F4F4F2F4-%&GAMMAG6#,&*&F1F2%#nuGF4F4*&F1F2F3F4F4F4)*&F :F4F3F2,$*&F1F2F:F4F4F4-F66#F>F2-F66#,$*&F1F2F3F4F4F2)*&,&*&F3F4F+F4F4 F:F4F4F3F2,&*&F1F2F:F4F2*&F1F2F3F4F2F42F)F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "assume(u>0);\nsimplify(\n(subs(nu=n1,omega=n2,A)\n /subs(omega=n1,nu=n2,B))\n,symbolic);\nu:='u';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uGF$" }}} }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 9 "Priklad 9" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "Nech\235 n\341hodn\341 veli\350ina X ~ t(n). Jak\351 rozlo\236en\355 m\341 transformovan\341 n\341hodn\341\nveli\350ina Y \+ = X2?" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "for i from 1 to 4 do\nX[i] := RandomVariable(Normal(0, 1));\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"XG6#\"\"\"%$_R3G" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>&%\"XG6#\"\"#%$_R4G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"XG6#\" \"$%$_R5G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"XG6#\"\"%%$_R6G" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "X[X] := _R6;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "i:='i';\nt:='t';\nY:= PDF(sqrt(sum( X[i]^2,i = 2 .. 4)),t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iGF$" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"tGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"YG-%*PIECEWISEG6$7$\"\"!1%\"tGF)7$,$*(\"\"#\"\"\"F+ F0-F&6$7$F)1*$)F+F/F0F)7$,$*&#F0F/F0**F5F:F/F:-%$expG6#,$*&F/!\"\"F+F/ FAF0%#PiG#FAF/F0F02F)F5F0F02F)F+" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 1 "2" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 10 "1. priklad" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Pravdepodobnost, \236e v\375robek m\341 1 . jakost, je " }{XPPEDIT 18 0 "nu = .9;" "6#/%#nuG-%&FloatG6$\"\"*!\" \"" }{TEXT -1 300 ". Kolik v\375robku je treba\nzkontrolovat, aby s pr avdepodobnost\355 aspon 0,99 bylo zaruceno, \236e rozd\355l relativn \355 cetnosti\npoctu v\375robku 1. jakosti a pravdepodobnosti ? = 0,9 \+ byl v absolutn\355 hodnote men\232\355 ne\236 0,03?\nK v\375poctu pou \236ijte jak Bernoulliovu vetu, tak Moivre-Laplaceovu vetu a v\375sled ky\nporovnejte." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "X := RandomVariable(Binomial(n,.9)) ;\nf:=ProbabilityFunction(X, u);\n#f:=t->Quantile(X, t,numeric);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG%$_R1G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG-%*PIECEWISEG6$7$\"\"!2%\"uGF)7$*(-%)binomialG6$% \"nGF+\"\"\")$\"\"*!\"\"F+F2)$F2F6,&F1F2F+F6F2%*otherwiseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "unapply(f,u)(X/n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%*PIECEWISEG6$7$\"\"!2*&%$_R1G\"\"\"%\"nG!\"\"F'7 $*(-%)binomialG6$F,F)F+)$\"\"*F-F)F+)$F+F-,&F,F+F)F-F+%*otherwiseG" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 1 "2" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 146 "Pravd\354podo bnost \372sp\354chu p\370i jednom pokusu je 0,3. S jakou pravd\354podo bnost\355\nlze tvrdit, \236e po\350et \372sp\354ch\371 ve 100 pokusech bude v mez\355ch od 20 do 40?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 68 "X := RandomVariable(Binomial(100,.3));\nf:=Pro babilityFunction(X, u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG%%_R6 0G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG-%*PIECEWISEG6$7$\"\"!2%\" uGF)7$*(-%)binomialG6$\"$+\"F+\"\"\")$\"\"$!\"\"F+F2)$\"\"(F6,&F1F2F+F 6F2%*otherwiseG" }}}{EXCHG {PARA 15 "" 0 "" {TEXT -1 4 "The " } {HYPERLNK 17 "Quantile" 2 "Statistics/Quantile" "" }{TEXT -1 265 " fun ction applied to a binomial distribution uses a sequence of iterations in order to converge upon the desired output point. The maximum numbe r of iterations to perform is equal to 100 by default, but this value \+ can be changed by setting the environment variable " }{TEXT 35 24 "_En vStatisticsIterations" }{TEXT -1 38 " to the desired number of iterati ons. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Quantile(f, 40);\n" }}{PARA 8 "" 1 "" {TEXT -1 106 "E rror, (in Statistics:-Quantile) unknown distribution: piecewise(u < 0, 0,binomial(100,u)*.3^u*.7^(100-u))\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "sum(f,u=20..40);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$ \"+XQ9'y*!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 1 "5" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 156 "Pravd\354podobnost narozen\355 chlapce je 0,515. Jak\341 je pr avd\354podobnost, \236e mezi 10\n000 novorozenci bude\na) v\355ce d \354v\350at ne\236 chlapc\371\nb) chlapc\371 od 5 000 do 5 300?" }}} {SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "X := RandomVariable(Binomial(10000,.515));\nf:=Probab ilityFunction(X,u);\nsum(f,u=10000/2..10000);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"XG%%_R63G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG -%*PIECEWISEG6$7$\"\"!2%\"uGF)7$*(-%)binomialG6$\"&++\"F+\"\"\")$\"$:& !\"$F+F2)$\"$&[F6,&F1F2F+!\"\"F2%*otherwiseG" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warning, computation interrupted\n" }}}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "2 9 4" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }