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The Poisson distribution is used to model " }{TEXT 203 0 "" }}{PARA 201 "" 0 "" {TEXT 203 76 "the data. The few \"greate r or equal to 10'' intervals are grouped together." }{TEXT 203 0 "" }} }{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 204 14 "with(plots): " }} {PARA 203 "" 1 "" {TEXT 205 49 "Warning, the name changecoords has bee n redefined" }{TEXT 205 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 206 53 "p:= (j,lambda) -> exp(-lambda)*lambda^j/factorial(j);" } {MPLTEXT 1 204 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>I\"pG6\"f*6$I \"jGF%I'lambdaGF%F%6$I)operatorGF%I&arrowGF%F%*(-I$expGF%6#,$9%!\"\"\" \"\")F29$F4-I*factorialGI*protectedGF96#F6F3F%F%F%" }{TEXT 207 0 "" }} }{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 206 10 "n[0]:=57; " }{MPLTEXT 1 206 45 "n[1]:=203; n[2]:= 383; n[3]:= 525; n[4]:=532;" }{MPLTEXT 1 204 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 206 58 "n[5]:= 408; n[6] := \+ 273; n[7]:= 139; n[8]:= 45; n[9]:= 27;" }{MPLTEXT 1 204 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 206 40 "n[10]:= 16;# at least 10 alpha-partic les" }{MPLTEXT 1 204 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"nG6 \"6#\"\"!\"#d" }{TEXT 207 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I \"nG6\"6#\"\"\"\"$.#" }{TEXT 207 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"nG6\"6#\"\"#\"$$Q" }{TEXT 207 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"nG6\"6#\"\"$\"$D&" }{TEXT 207 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"nG6\"6#\"\"%\"$K&" }{TEXT 207 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"nG6\"6#\"\"&\"$3%" }{TEXT 207 0 "" }} {PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"nG6\"6#\"\"'\"$t#" }{TEXT 207 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"nG6\"6#\"\"(\"$R\"" }{TEXT 207 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"nG6\"6#\"\")\"#X" } {TEXT 207 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"nG6\"6#\"\"*\"# F" }{TEXT 207 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"nG6\"6#\"#5 \"#;" }{TEXT 207 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 206 18 "sum(n[k],k=0..10);" }{MPLTEXT 1 204 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#\"%3E" }{TEXT 207 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 206 67 "approxLambda :=evalf(sum(k*n[k],k=0..10)/2608);#est imate for lambda" }{MPLTEXT 1 204 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>I-approxLambdaG6\"$\"+)GJt'Q!\"*" }{TEXT 207 0 "" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 203 33 "Let's actually compare the values" } {TEXT 203 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 206 20 "for k \+ from 0 to 9 do" }{MPLTEXT 1 204 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 206 131 "print(\"the number of intervals with \",k,\" clicks was \",n[ k],\" : the Poisson model predicts \",evalf[4](2608*p(k,approxLambda)) ); od;" }{MPLTEXT 1 204 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6(Q>the~ number~of~intervals~with~6\"\"\"!Q-~clicks~was~F$\"#dQ?~:~the~Poisson~ model~predicts~F$$\"%ca!\"#" }{TEXT 207 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6(Q>the~number~of~intervals~with~6\"\"\"\"Q-~clicks~was~F $\"$.#Q?~:~the~Poisson~model~predicts~F$$\"%5@!\"\"" }{TEXT 207 0 "" } }{PARA 204 "" 1 "" {XPPMATH 20 "6(Q>the~number~of~intervals~with~6\"\" \"#Q-~clicks~was~F$\"$$QQ?~:~the~Poisson~model~predicts~F$$\"%zS!\"\"" }{TEXT 207 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6(Q>the~number~of~in tervals~with~6\"\"\"$Q-~clicks~was~F$\"$D&Q?~:~the~Poisson~model~predi cts~F$$\"%g_!\"\"" }{TEXT 207 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6( Q>the~number~of~intervals~with~6\"\"\"%Q-~clicks~was~F$\"$K&Q?~:~the~P oisson~model~predicts~F$$\"%$3&!\"\"" }{TEXT 207 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6(Q>the~number~of~intervals~with~6\"\"\"&Q-~clicks~w as~F$\"$3%Q?~:~the~Poisson~model~predicts~F$$\"%LR!\"\"" }{TEXT 207 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6(Q>the~number~of~intervals~with~6 \"\"\"'Q-~clicks~was~F$\"$t#Q?~:~the~Poisson~model~predicts~F$$\"%MD! \"\"" }{TEXT 207 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6(Q>the~number~ of~intervals~with~6\"\"\"(Q-~clicks~was~F$\"$R\"Q?~:~the~Poisson~model ~predicts~F$$\"%+9!\"\"" }{TEXT 207 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6(Q>the~number~of~intervals~with~6\"\"\")Q-~clicks~was~F$\"#XQ?~:~ the~Poisson~model~predicts~F$$\"%ln!\"#" }{TEXT 207 0 "" }}{PARA 204 " " 1 "" {XPPMATH 20 "6(Q>the~number~of~intervals~with~6\"\"\"*Q-~clicks ~was~F$\"#FQ?~:~the~Poisson~model~predicts~F$$\"%3H!\"#" }{TEXT 207 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 204 37 "A:=listplot([seq([ j,n[j]],j=0..10)]):" }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 202 "> " 0 " " {MPLTEXT 1 204 21 "B:= listplot([seq([j," }{MPLTEXT 1 206 5 "2608*" }{MPLTEXT 1 204 5 "exp(-" }{MPLTEXT 1 206 12 "approxLambda" }{MPLTEXT 1 204 2 ")*" }{MPLTEXT 1 206 12 "approxLambda" }{MPLTEXT 1 204 18 "^j/ j!],j=0..10)]):" }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 204 15 "display(\{A,B\});" }{MPLTEXT 1 204 0 "" }}{PARA 205 "" 1 "" {GLPLOT2D 374 371 371 {PLOTDATA 2 "6$-%'CURVESG6#7-7$$\"\" !F)$\"#dF)7$$\"\"\"F)$\"$.#F)7$$\"\"#F)$\"$$QF)7$$\"\"$F)$\"$D&F)7$$\" \"%F)$\"$K&F)7$$\"\"&F)$\"$3%F)7$$\"\"'F)$\"$t#F)7$$\"\"(F)$\"$R\"F)7$ $\"\")F)$\"#XF)7$$\"\"*F)$\"#FF)7$$\"#5F)$\"#;F)-F$6#7-7$F($\"+i&*Raa! \")7$F-$\"+3qR4@!\"(7$F2$\"+D&o)ySFbo7$F7$\"+b>6e_Fbo7$F<$\"+>_r$3&Fbo 7$FA$\"+(=#3KRFbo7$FF$\"+ySWMDFbo7$FK$\"+o#>-S\"Fbo7$FP$\"+L(*))onF^o7 $FU$\"+\\ah3HF^o7$FZ$\"+`z&[7\"F^o" 1 2 2 0 10 1 2 6 1 4 2 1.0 45.0 45.0 1 0 "Curve 1" "Curve 2" }}{TEXT 208 0 "" }}}{EXCHG {PAGEBK }} {EXCHG {PARA 200 "" 0 "" {TEXT 202 19 "chi-square analysis" }{TEXT 202 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 204 26 "chisquare9:= sum((2608*p(j," }{MPLTEXT 1 206 23 "approxLambda)-n[j])^2/(" } {MPLTEXT 1 204 9 "2608*p(j," }{MPLTEXT 1 206 23 "approxLambda)),j=0..9 )+" }{MPLTEXT 1 204 18 "\n(2608*(1-sum(p(j," }{MPLTEXT 1 206 32 "appro xLambda),j=0..9))-n[10])^2/" }{MPLTEXT 1 204 17 "(2608*(1-sum(p(j," } {MPLTEXT 1 206 23 "approxLambda),j=0..9)))" }{MPLTEXT 1 206 1 ";" } {MPLTEXT 1 204 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>I+chisquare9G6 \"$\"+*GX8H\"!\")" }{TEXT 207 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 204 48 "1-stats[statevalf,cdf,chisquare[9]](chisquare9);" } {MPLTEXT 1 204 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#$\"+Iphl;!#5" } {TEXT 207 0 "" }}}{EXCHG {PARA 200 "" 0 "" {TEXT 202 102 "so 16.7% of \+ similar data samples from a Poisson distribution would have a larger c hi-square statistic." }{TEXT 202 0 "" }}}{PARA 206 "" 0 "" {TEXT 210 0 "" }}{PARA 206 "" 0 "" {TEXT 210 0 "" }}{PARA 206 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 15 10 1804 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }