Warscheinlichkeit / Kombinatorik Niggli:# binf, binF: Binomialverteilung
# Z\344hldichte b(n,p;k), V-Funktion F(n,p;k)binf := proc(n,p,k)
return evalf( binomial(n,k)*p^k*(1-p)^(n-k) );
end proc:binF := proc(n,p,k)
local i;
return evalf( sum(binf(n,p,i),i=0..k) );
end proc:# hypf, hypF: Hypergeometrische Verteilung
# Z\344hldichte h(N,K,n;k), V-Funktion F(N,K,n;k)hypf := proc(N,K,n,k)
return evalf( binomial(K,k)*binomial(N-K,n-k)/binomial(N,n) );
end proc:hypF := proc(N,K,n,k)
local i;
return evalf( sum(hypf(N,K,n,i),i=0..k) );
end proc:# poif, poiF: Poisson-Verteilung
# Z\344hldichte pi(lambda;k), V-Funktion F(lambda;k)poif := proc(la,k)
return evalf( exp(-la)*la^k/k! );
end proc:poiF := proc(la,k)
local i;
return evalf( sum(poif(la,i),i=0..k) );
end proc:with(plots, listplot): Binomial / Poisson:BP:=proc() local b, n, p, k, Po;
interface(prompt="Enter the number of trials: "); n:=parse(readline(),statement); interface(prompt="Enter the probability of success: "); p:=parse(readline(),statement); interface(prompt="Enter the number of successes: "); k:=parse(readline(),statement);
interface(prompt="> "); b:=(n,p,k)->binomial(n,k)*p^k*(1-p)^(n-k); Po:=(lambda,k)->lambda^k/k!*exp(-lambda); print(Binomial=evalf(b(n,p,k)), Poisson=evalf(Po(n*p,k)))
end:BP();A1a:=hypF(200,30,20,5);A1a2:=hypf(200,30,20,5);A1b:=1-hypF(200,30,20,11);A1c:=hypF(200,30,20,4);A1d:=hypf(200,30,20,0);250*0.39;A2b:=hypf(250,250*.39,250,124);1000/30;A3a:=poif(100/3,20);A3b:=poiF(100/3,21);A3c:=1-poiF(20,30);A6:=1-hypF(500,1,365,0);11/210;A4a:=binf(150,11/210,10);A4b:=binf(150,18/210,33)+binf(150,19/210,33)+binf(150,20/210,33);A4c:=binf(150,2/210,44)+binf(150,3/210,44)+binf(150,7/210,4)+binf(150,11/210,44)+binf(150,13/210,44)+binf(150,17/210,4)+binf(150,19/210,4)+binf(150,5/210,4);