restart;

Merkmalsraum := "{1,2,3,..,365}^n";

NiM+SS1NZXJrbWFsc3JhdW1HNiJRMXxmcjEsMiwzLC4uLDM2NXxocl5uRiU=

#GegenereignisK:=(n)->binomial(365,n);

NiM+SSJLRzYiZio2I0kibkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkpYmlub21pYWxHRiU2JCIkbCQ5JEYlRiVGJQ==

#Anzahl VariationenV:=(n)->n!*binomial(365,n);

NiM+SSJWRzYiZio2I0kibkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYtSSpmYWN0b3JpYWxHSSpwcm90ZWN0ZWRHRi82IzkkIiIiLUkpYmlub21pYWxHRiU2JCIkbCRGMUYyRiVGJUYl

# |Lambda|anz:=(n)->365^n;

NiM+SSRhbnpHNiJmKjYjSSJuR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUpIiRsJDkkRiVGJUYl

P:=(n)->evalf(V(n)/anz(n));

NiM+SSJQRzYiZio2I0kibkdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkmZXZhbGZHSSpwcm90ZWN0ZWRHRi42IyomLUkiVkdGJTYjOSQiIiItSSRhbnpHRiVGMyEiIkYlRiVGJQ==

NiM+SSJQRzYiZio2I0kibkdGJTciNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYtSSpmYWN0b3JpYWxHSSpwcm90ZWN0ZWRHRjA2IyIkbCQiIiIqJiksJkYyRjNGKCEiIkYoRjMpRjJGKEYzRjdGJUYlRiU=

1-P(25);

NiMkIitTcSpwbyYhIzU=

1-P(50);

NiMkIisnek5QcSohIzU=

Tardy:= (x) -> evalf(1 - product((365-i)/(365), i=0..x-1));

NiM+SSZUYXJkeUc2ImYqNiNJInhHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJS1JJmV2YWxmR0kqcHJvdGVjdGVkR0YuNiMsJiIiIkYxLUkocHJvZHVjdEc2JEYuSShfc3lzbGliR0YlNiQsJkYxRjFJImlHRiUjISIiIiRsJC9GODsiIiEsJjkkRjFGOkYxRjpGJUYlRiU=

Tardy(25);

NiMkIitTcSpwbyYhIzU=

Tardy(50);

NiMkIisnek5QcSohIzU=

restart;p:=0.5;

NiM+SSJwRzYiJCIiJiEiIg==

binom:=(n,p,k)->binomial(n,k)*p^k*(1-p)^(n-k);

NiM+SSZiaW5vbUc2ImYqNiVJIm5HRiVJInBHRiVJImtHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSooLUkpYmlub21pYWxHRiU2JDkkOSYiIiIpOSVGM0Y0KSwmRjRGNEY2ISIiLCZGMkY0RjNGOUY0RiVGJUYl

binom(4,0.5,2);

NiMkIiVdUCEiJQ==

binom(4,0.5,3);

NiMkIiUrRCEiJQ==

binom(4,0.5,4);

NiMkIiREJyEiJQ==

restart;binom:=(n,p,k)->binomial(n,k)*p^k*(1-p)^(n-k);

NiM+SSZiaW5vbUc2ImYqNiVJIm5HRiVJInBHRiVJImtHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSooLUkpYmlub21pYWxHRiU2JDkkOSYiIiIpOSVGM0Y0KSwmRjRGNEY2ISIiLCZGMkY0RjNGOUY0RiVGJUYl

#poisson lambda = n * p#nur ein parameterpois:=(n,p,k)->exp(-(n*p))*((n*p)^k/k!);

NiM+SSVwb2lzRzYiZio2JUkibkdGJUkicEdGJUkia0dGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKigtSSRleHBHRiU2IywkKiY5JCIiIjklRjUhIiJGNSlGMzkmRjUtSSpmYWN0b3JpYWxHSSpwcm90ZWN0ZWRHRjw2I0Y5RjdGJUYlRiU=

binom(2500,0.003,1);

NiMkIitPcyhSNiUhIzc=

binom(2500,0.003,5);

NiMkIis3KnBNNCIhIzU=

binom(2500,0.003,10);

NiMkIitEVFoqZSkhIzY=

binom(2500,0.003,20);

NiMkIiskeWtYLCghIzk=

pois(2500,0.003,1);

NiMkIit3RjhbVCEjNw==

pois(2500,0.003,5);

NiMkIitaZnUkNCIhIzU=

pois(2500,0.003,10);

NiMkIitTcS4kZSkhIzY=

pois(2500,0.003,20);

NiMkIishUSNHNHMhIzk=

1-sum(binom(2500,0.003,i),i=0..9);

NiMkIitxRE1MQSEjNQ==

1-sum(binom(2500,0.003,i),i=0..19);

NiMkIih5WTIiISM1

1-sum(pois(2500,0.003,i),i=0..9);

NiMkIitxUSNmQiMhIzU=

1-sum(pois(2500,0.003,i),i=0..19);

NiMkIignXDI2ISM1

sum(binom(2500,0.003,i),i=0..10);

NiMkIitVW2dEJykhIzU=

sum(binom(2500,0.003,i),i=0..20);

NiMkIit5bmkqKioqISM1

sum(pois(2500,0.003,i),i=0..10);

NiMkIitNKXpCaSkhIzU=

sum(pois(2500,0.003,i),i=0..20);

NiMkIitMTWgqKioqISM1

restart;pois:=(lambda,k)->exp(-lambda)*(lambda^k/k!);

NiM+SSVwb2lzRzYiZio2JEknbGFtYmRhR0YlSSJrR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUqKC1JJGV4cEdGJTYjLCQ5JCEiIiIiIilGMjklRjQtSSpmYWN0b3JpYWxHSSpwcm90ZWN0ZWRHRjk2I0Y2RjNGJUYlRiU=

evalf(1-sum(pois(10,i),i=0..10));

NiMkIisrRGdwVCEjNQ==

evalf(1-sum(pois(10,i),i=0..20));

NiMkIikwRSllIiEjNQ==

evalf(1-sum(pois(15,i),i=0..10));

NiMkIismKWVOOikpISM1

evalf(1-sum(pois(15,i),i=0..20));

NiMkIiosIjQoSCkhIzU=

restart;hyper:=(N,K,n,k)->(binomial(K,k)*binomial(N-K,n-k))/binomial(N,n);

NiM+SSZoeXBlckc2ImYqNiZJIk5HRiVJIktHRiVJIm5HRiVJImtHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSooLUkpYmlub21pYWxHRiU2JDklOSciIiItRjE2JCwmOSRGNUYzISIiLCY5JkY1RjRGOkY1LUYxNiRGOUY8RjpGJUYlRiU=

plot(hyper(x,300,50,8), x=1873..1876);

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

evalf(hyper(1874,300,50,8));

NiMkIishM01LYSIhIzU=

evalf(hyper(1875,300,50,8));

NiMkIishM01LYSIhIzU=

# ==> 1880

restart;binom:=(n,p,k)->binomial(n,k)*p^k*(1-p)^(n-k);

NiM+SSZiaW5vbUc2ImYqNiVJIm5HRiVJInBHRiVJImtHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSooLUkpYmlub21pYWxHRiU2JDkkOSYiIiIpOSVGM0Y0KSwmRjRGNEY2ISIiLCZGMkY0RjNGOUY0RiVGJUYl

evalf(1-sum(binom(1000,0.01,i),i=0..10));

NiMkIituPmZwVCEjNQ==

evalf(1-sum(binom(1000,0.01,i),i=0..20));

NiMkIik6WydcIiEjNQ==

restart;binom:=(n,p,k)->binomial(n,k)*p^k*(1-p)^(n-k);

NiM+SSZiaW5vbUc2ImYqNiVJIm5HRiVJInBHRiVJImtHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSooLUkpYmlub21pYWxHNiRJKnByb3RlY3RlZEdGMkkoX3N5c2xpYkdGJTYkOSQ5JiIiIik5JUY2RjcpLCZGN0Y3RjkhIiIsJkY1RjdGNkY8RjdGJUYlRiU=

hyper:=(N,K,n,k)->(binomial(K,k)*binomial(N-K,n-k))/binomial(N,n);

NiM+SSZoeXBlckc2ImYqNiZJIk5HRiVJIktHRiVJIm5HRiVJImtHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSooLUkpYmlub21pYWxHNiRJKnByb3RlY3RlZEdGM0koX3N5c2xpYkdGJTYkOSU5JyIiIi1GMTYkLCY5JEY4RjYhIiIsJjkmRjhGN0Y9RjgtRjE2JEY8Rj9GPUYlRiVGJQ==

evalf(1-hyper(100,5,10,0));

NiMkIitKalppVCEjNQ==