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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(stats[random]):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 245 "n:=1000:\np:=0.5:  #th
e disease prevalence rate\na:=0.05:   #the rate of false negatives\nb:
=0.05:   #the rate of false positives\ns:=stats[random, binomiald[1,p]
](n):\n#s contains the disease status of the n patients (0 - non-suffe
rer, 1 - sufferer)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 482 "#Now
 simulate the test results for the n patients\n#The results will be pl
aced in t\nfor i from 1 by 1 while i < n+1 do\n   #and only change the
 test result according to the \"error rate\"\n   #probabilities a and \+
b\n   #simulate the false negatives - Test negative, given a sufferer \+
\n   if s[i] = 1.0 then t[i]:=stats[random,binomiald[1,1-a]](1) fi:\n \+
  #simulate the false positives - Test positive, given a non-sufferer
\n   if s[i] = 0.0 then t[i]:=stats[random,binomiald[1,b]](1) fi:\nod:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 390 "#Now count the positiv
e test results, the total number of sufferers,\n#and those who test po
sitive and are actually sufferers\ntotalpositive:=0:\ntotalsuff:=0:\nt
otalpossuff:=0:\nfor i from 1 by 1 while i < n+1 do\n   if(t[i] = 1.0)
 then totalpositive:=totalpositive+1 fi:\n   if(s[i] = 1.0) then total
suff:=totalsuff+1 fi:\n   if s[i] = 1.0 and t[i] = 1.0 then totalpossu
ff:=totalpossuff+1 fi:\nod:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
14 "totalpositive;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$t%" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "totalsuff;" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#\"$t%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "
totalpossuff;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$V%" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "#Hence the number of false positive
 results is\ntotalpositive-totalpossuff;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"#I" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "#The actual p
robability of a positive result is\nprobpositive:=(1-a)*p+b*(1-p);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%-probpositiveG$\"$+&!\"$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "#whereas in the sample, the proport
ion if\nconvert(totalpositive/n,float);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#$\"++++IZ!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 144 "#The
 actual posterior probability of the patient being a sufferer is\n#giv
en a test positive result is\nposteriorprob:=(1-a)*p/((1-a)*p+b*(1-p))
;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%.posteriorprobG$\"+++++&*!#5
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "#whereas the proportion
 in the sample is\nconvert(totalpossuff/totalpositive,float);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+H0vl$*!#5" }}}{EXCHG {PARA 0 "> " 
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1803 }