{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "#\n# Einfacher Pr \374fplan mit abgebrochener Kontrolle\n# Sch\366ne Formel f\374r E(n_d ach)\n#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 195 "#\n# Hypergeome trische Verteilung H(N,M,n)\n# Ai = \{Pr\374fung bricht ab genau im Sc hritt i\}\n# Gilt die Beziehung: \n# P(Ai) = P\{H(N,M,i-1) = c\}*(M -c)/(N-i+1)\n# = (M/N)*P\{H(N-1,M-1,i-1) = c\}" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 69 "A:=((M-c)/(N-i+1))*binomial(M,c)*binomial(N-M,i-1-c )/binomial(N,i-1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "B:=(M /N)*binomial(M-1,c)*binomial(N-M,i-1-c)/binomial(N-1,i-1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "A-B;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "expand(%);" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "#\n# Gilt die sch\366ne Formel f \374r den Erwartungswert?\n#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "N:=5000;" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "M:=50;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 7 "n:=303;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "c:=5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "# \n# Definition der Funktion: p(i) = P(Ai)" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 70 "p := i -> (M/N)*binomial(M-1,c)*binomial(N-M,i-1-c) /binomial(N-1,i-1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "S1:= sum(i*p(i),i=c+1..n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "# \+ P(Xplus > c+1)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "prob := s um(binomial(M+1,k)*binomial(N-M,n+1-k)/binomial(N+1,n+1),k=c+2..n);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "S2:=prob*(c+1)*(N+1)/(M+1) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "S1-S2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "14 0 0" 41 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }