<Text-field layout="Heading 1" style="Heading 1">Uebung 8</Text-field>

<Text-field layout="Heading 2" style="Heading 2">Funktionen</Text-field>

# 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:

# norf, norF: Normalverteilung # Dichtefunktion f(a,sig;x), v-Funktion F(a,sig;x)

norf := (a,sig,x) -> evalf(1/(sig*sqrt(2*Pi)))*exp((-1/2)*((x-a)/sig)^2):

norF := (a,sig,x) -> evalf( int(norf(a,sig,t),t=-infinity..x)):

<Text-field layout="Heading 2" style="Heading 2">Aufgabe 1</Text-field>

restart;

a:=12;

NiM+SSJhRzYiIiM3

sig2:=4;

NiM+SSVzaWcyRzYiIiIl

sig:=sqrt(sig2);

NiM+SSRzaWdHNiIiIiM=

plot([norf(a,sig,x), norF(a,sig,x)],x=6..18);

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

<Text-field layout="Heading 3" style="Heading 3">a)</Text-field>

100*(1-norF(a,sig,10));

NiMkIitodVc4JSkhIik=

<Text-field layout="Heading 3" style="Heading 3">b)</Text-field>

100*norF(a,sig,8);

NiMkIitxSix2QSEiKg==

<Text-field layout="Heading 3" style="Heading 3">c)</Text-field>

100*(norF(a,sig,16)-norF(a,sig,9));

NiMkIitqbVUvIiohIik=

<Text-field layout="Heading 3" style="Heading 3">d)</Text-field>

100*(norF(a,sig,14)-norF(a,sig,6));

NiMkIit0JVsqKlIpISIp

<Text-field layout="Heading 2" style="Heading 2">Aufgabe 2</Text-field>

restart;

a:=-2;

NiM+SSJhRzYiISIj

sig2:=0.25;

NiM+SSVzaWcyRzYiJCIjRCEiIw==

sig:=sqrt(sig2);

NiM+SSRzaWdHNiIkIisrKysrXSEjNQ==

plot([norf(a,sig,x),norF(a,sig,x)], x=-5..1);

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

<Text-field layout="Heading 3" style="Heading 3">a)</Text-field>

d:=fsolve(1-norF(a,sig,c)=0.44,c=-1.8);

NiM+SSJkRzYiJCErI1I6WCM+ISIq

d:=fsolve(1-norF(a,sig,c)=0.44,c);

NiM+SSJkRzYiJCErI1I6WCM+ISIq

100*(1-norF(a,sig,d));

NiMkIisrKysrVyEiKQ==

<Text-field layout="Heading 3" style="Heading 3">b)</Text-field>

e:=fsolve(norF(a,sig,c)=0.2,c);

NiM+SSJlRzYiJCErPDEiM1UjISIq

100*(norF(a,sig,e));

NiMkIispKioqKioqKj4hIik=

<Text-field layout="Heading 2" style="Heading 2">Aufgabe 3</Text-field>

<Text-field layout="Heading 3" style="Heading 3">a)</Text-field>

restart;

a:=0;

NiM+SSJhRzYiIiIh

sig:=1;

NiM+SSRzaWdHNiIiIiI=

plot([norf(a,sig,x),norF(a,sig,x)], x=-5..5);

LSUlUExPVEc2Ji0lJ0NVUlZFU0c2JTdlbzckJCEiJiIiISQiMyZ5aSQpUl4+blsiISNCNyQkITNZTExMZSVHP3klISM8JCIzKG9obGp6KVs8VkYvNyQkITNRbW1UJmVzQmYlRjMkIjNXKilvYDNsRV01ISNBNyQkITNBTEwkM3MlM3pWRjMkIjMkKjMnb0I+IjNNRkY7NyQkITNeTEwkZS8kUWtURjMkIjN1LXlebnoxVG9GOzckJCEzb21tVDU9cV1SRjMkIjNzQXFvUVUvRzshI0A3JCQhM0lMTDNfPmZfUEYzJCIzJVJYbFhXUj1cJEZLNyQkITNLKyt2bzFZWk5GMyQiM11vQjw+ZShHUShGSzckJCEzO0xMMy1PSk5MRjMkIjMpSDVuWDRIQGAiISM/NyQkITNwKioqXFAqbyVRNyRGMyQiM28qNGMmUmk7TElGZW43JCQhM0ttbW0iUkZqIUhGMyQiMzdHaTxHZT1XZUZlbjckJCEzM0xMJGU0T1pyI0YzJCIzbHBBZzRsTCw1ISM+NyQkITN3KioqKipcblwhKlwjRjMkIjNcYFdYLCcpKnB2IkZlbzckJCEzJikqKioqKlxpeENHI0YzJCIzbGVLY0dbdVtIRmVvNyQkITMiKioqKioqXEtxUDIjRjMkIjNXUzA8cCdIZWslRmVvNyQkITM6TEwzLVRDJSk9RjMkIjNQIj1CdyE0OWduRmVvNyQkITNabW1tIjR6KWU7RjMkIjNYR1laNmt0MjUhIz03JCQhM1NtbTtIQVVqOkYzJCIzeSdvOCNSW0Z2NkZfcTckJCEzTG1tbW1gJ3pZIkYzJCIzZGVlUCtUQmU4Rl9xNyQkITM3TCQzRk1FcE4iRjMkIjMiemxhQUpvKSllIkZfcTckJCEzIyoqKipcKD10KWVDIkYzJCIzKCpbUyo+QSopZSQ9Rl9xNyQkITNPTCQzeCcqKWZaNkYzJCIzRC5RN3gzMGw/Rl9xNyQkITMib21tbWg1JFw1RjMkIjNFUVYvcGFbK0JGX3E3JCQhM3RJTDN4cnM5JSpGX3EkIjNnTGNsXEA7aERGX3E3JCQhM1MkKioqXCg9W2pMKUZfcSQiM0hqLEJXL1Q9R0ZfcTckJCEzcSUqKioqXFB3JTR0Rl9xJCIzJ3kqM1EuI2ZUMCRGX3E3JCQhMypmKioqXGlYZyNHJ0ZfcSQiM25iJkcsKD0iXEYkRl9xNyQkITMkb0skM186PDZfRl9xJCIzJyk0J3leMioqR1skRl9xNyQkITNuZG1tVCZRKFJURl9xJCIzIT5AQVRuOz1tJEZfcTckJCEzSWhtIkhkR2U6JEZfcSQiMykpSC1CaCZIY3okRl9xNyQkITMkXG1tVGc9PjwjRl9xJCIzKyllNXBtR2sqUUZfcTckJCEzRkskM0ZweTdrIkZfcSQiMzJ4MEUqZlxnJFJGX3E3JCQhM2cqKipcN3lRMTYiRl9xJCIzeF9sRSpRJCpbJ1JGX3E3JCQhM2hLJDNfRCk9YCUpRmVvJCIzMDx3TllaPnZSRl9xNyQkITNFcG0ienApKSoqeiZGZW8kIjN4JHl4IWYjPUYpUkZfcTckJCEzI2YrRDE5KnlZSkZlbyQiMycpMyZSOTJbdSlSRl9xNyQkITN1RE1MTGUqZSRcRmVuJCIzWkxyKzBVUCopUkZfcTckJCIzKlxtVCYpM1JCRSNGZW8kIjNBRCx6Lj9TKSlSRl9xNyQkIjNic21UZ3hFPV1GZW8kIjNPeS1CekVTJSlSRl9xNyQkIjM3IW8iSEtrPnV4RmVvJCIzL1AheWtMJlF4UkZfcTckJCIzd29tVDVELGA1Rl9xJCIzUmUwKnAkZk9uUkZfcTckJCIzR3E7elcjKT4vO0ZfcSQiM05jbGQxKD0lUVJGX3E3JCQiM3pybTt6UlFiQEZfcSQiMzMtOikqcEcjeSpRRl9xNyQkIjNsT0xMJGUsXTYkRl9xJCIzMCZHYTVXIlwrUUZfcTckJCIzXywrXSg9PlkyJUZfcSQiMzInNGM9Y0I7biRGX3E3JCQiMzZRTGUqW0s1NiZGX3EkIjNKI0dRaUVZNF0kRl9xNyQkIjNydW1tInpYdTknRl9xJCIzbFBDcSRcUERJJEZfcTckJCIzI3lMTGU5aSI9c0ZfcSQiMyQqRyo0NFolW3VJRl9xNyQkIjMkNCsrK115KSlHKUZfcSQiM1QoPkVIeWAmSEdGX3E3JCQiMyU+KytEY2xqTCpGX3EkIjNVRlpVaHkvIWUjRl9xNyQkIjNIKytdaV9RUTVGMyQiM3AyZVc7OChvSyNGX3E3JCQiM1UrXSg9LU4oUjZGMyQiMyRmPS5zOzJQMyNGX3E3JCQiM2IrK0QieSUzVDdGMyQiMzBLUiYpXGQpbyU9Rl9xNyQkIjNGK11QNGtoYDhGMyQiM00mRygqKmY8LCdmIkZfcTckJCIzLCsrXVAhW2hZIkYzJCIzMXlZeWAsJz1PIkZfcTckJCIzS21tVDVGRW46RjMkIjMlW3o1OW5JI282Rl9xNyQkIjNqS0xMJFF4JG87RjMkIjNpd3NhKSlvUD4qKkZlbzckJCIzWisrK3YuSSUpPUYzJCIzeSlcZlU5QyVmbkZlbzckJCIzQG1tInpwZSp6P0YzJCIzMUpVbUE7XSdlJUZlbzckJCIzOywrK0RcJ1FII0YzJCIzcFReNi5XIUgoR0ZlbzckJCIzJ0hMJGU5UzgmXCNGMyQiMyR6Ukg7UWlVeCJGZW83JCQiM3MrK0QxIz1icSNGMyQiM2BYT1ZGbW1FNUZlbzckJCIzIkhMTCQzcz82SEYzJCIzNCZwL1wleiI9dyZGZW43JCQiM2EqKipcN2BXbDckRjMkIjM3IT1iOD0teCskRmVuNyQkIjNlbm1tbSpSUkwkRjMkIjNYTVAjUT9qIlI6RmVuNyQkIjMlem1tVHZKZ2EkRjMkIjNhdCEpKXo9KFE/dUZLNyQkIjNeTUxlOXRPY1BGMyQiMydlTipSQ01wVU1GSzckJCIzMSwrK11Ra1xSRjMkIjMkKTQiKkh5QSdbaiJGSzckJCIzIVtMTDNkZzY8JUYzJCIzUjcyXlUzYF1tRjs3JCQiMyZ5bW1tdyhHcFZGMyQiMzkmSDwqSE16YEdGOzckJCIzQysrRCJvSzBlJUYzJCIzUFpkXFZpKCkzNkY7NyQkIjM2LCt2PTVzI3klRjMkIjNgc1JIb0RALlZGLzckJCIiJkYsRi03UzckRiokIjM/bjZQT2RebUchI0M3JEYxJCIzNl9hTlBfdncnKUZqYmw3JEY3JCIzW1JIJlxPdjY+I0YvNyRGPSQiM3MzW0xoKVIqZWZGLzckRkIkIjNWLlt0UCF5NGMiRjs3JEZHJCIzSzkiW2cuPWgqUUY7NyRGTSQiM04jZVJcRCF5XSgpRjs3JEZSJCIzUigqSEVAIj5bJT5GSzckRlckIjNVbmtNckU7Z1VGSzckRmduJCIzcTFGJUhybF4jKilGSzckRlxvJCIzdyJ6UyoqKkhcRz1GZW43JEZhbyQiMzYkKmYoKVwsVjtMRmVuNyRGZ28kIjM0KFtmYHJVakEnRmVuNyRGXHAkIjNXIypcXF55MEI2RmVvNyRGYXAkIjMmPiZbJzNLS10hPkZlbzckRmZwJCIzZWhBVUkjKWZ3SEZlbzckRltxJCIzJzRCazIkeitkW0ZlbzckRmZxJCIzeE5bcU06bzByRmVvNyRGYHIkIjMkUlRTOSQpR1MxIkZfcTckRmpyJCIzVkVpJ2YhZjxxOUZfcTckRmRzJCIzPShbO0EqUlZBP0ZfcTckRl50JCIzY2RbSmRtO1xFRl9xNyRGaHQkIjM7QS1lc2lZJVIkRl9xNyRGYnUkIjM8cSIzYzglSFNURl9xNyRGYHckIjMmeic+ZSsoMy4pXEZfcTckRl55JCIzZS4sby5ARWBlRl9xNyRGaHkkIjNsXScpby9pbCJlJ0ZfcTckRmJ6JCIzKSpcRiUzI0hRMXRGX3E3JEZcW2wkIjMuX2o7UDE7a3pGX3E3JEZmW2wkIjNqL1BxX2phLyYpRl9xNyRGYFxsJCIzUDhEUlB5N0YqKUZfcTckRmpcbCQiM3VTNysnPWdwRypGX3E3JEZkXWwkIjNNQk1rO2V6QiYqRl9xNyRGaV1sJCIzWFNjQTMjeUJxKkZfcTckRl5ebCQiMyR5W2JeUWBCIikqRl9xNyRGY15sJCIzX1NaWSlwMzUqKSpGX3E3JEZoXmwkIjNVXHhfM18vUCoqRl9xNyRGXV9sJCIzeWEqUnEuLGYnKipGX3E3JEZiX2wkIjN6aD1tTCMpKj4pKipGX3E3JEZnX2wkIjMrYyo+aUljNioqKkZfcTckRlxgbCQiMz8qeSM9Tig9ZCoqKkZfcTckRmFgbCQiM2ddLmcnZlchKSoqKkZfcTckRmZgbCQiMz8vJ2VSK1EiKioqKkZfcTckRlthbCQiMyU0eCY9YSczJyoqKipGX3E3JEZgYWwkIjNZIT0jKmVZWykqKioqRl9xNyRGZWFsJCIzX0Iyemx3JCoqKioqRl9xNyRGamFsJCIzOWhLTS1vKCoqKioqRl9xNyRGX2JsJCIyJz5sNFg4KioqKioqRjM3JEZkYmwkIjJZRSVbRHIqKioqKipGMy0lJkNPTE9SRzYpJSRSR0JHJCIjNSEiIiRGLEZhXG1GYlxtRmJcbUZfXG1GYlxtLSUrQVhFU0xBQkVMU0c2JFEieDYiUSFGZ1xtLSUlRk9OVEc2JCUqSEVMVkVUSUNBR0ZgXG0tJSVWSUVXRzYkOyQhI11GYVxtJCIjXUZhXG07JCEyO01PbT1xKioqPkZfcSQiMk9PbTVxKioqPjUhIzs=

100*(norF(a,sig,a+sig)-norF(a,sig,a-sig));

NiMkIis5XCpvI28hIik=

100*(norF(a,sig,a+2*sig)-norF(a,sig,a-2*sig));

NiMkIithdCpcYSohIik=

100*(norF(a,sig,a+3*sig)-norF(a,sig,a-3*sig));

NiMkIitLPyt0KiohIik=

<Text-field layout="Heading 3" style="Heading 3">b)</Text-field>

a:=0;

NiM+SSJhRzYiIiIh

sig:=1;

NiM+SSRzaWdHNiIiIiI=

plot([norf(a,sig,x),norF(a,sig,x)], x=-5..5);

100*(norF(a,sig,a+1.96*sig)-norF(a,sig,a-1.96*sig));

NiMkIiskNFUrXSohIik=

100*(norF(a,sig,a+2.58*sig)-norF(a,sig,a-2.58*sig));

NiMkIit6Jyo+LCoqISIp

100*(norF(a,sig,a+3.29*sig)-norF(a,sig,a-3.29*sig));

NiMkIitkNykqKikqKiEiKQ==

<Text-field layout="Heading 2" style="Heading 2">Aufgabe 4</Text-field>

restart;

n:=100;

NiM+SSJuRzYiIiQrIg==

p:=1/2;

NiM+SSJwRzYiIyIiIiIiIw==

(a) Binomilaverteilung NiMvLSUiQkc2JCUibkclInBHLUYlNiQiJCsiKiYiIiJGLSIiIyEiIg== , ZV: X = 'Anzahl Erfolge'

Gesuchte Wahrscheinlichkeit: P( 40 < X <= 60 ) = NiMvLCYtJiUiRkc2IyUiQkc2IyIjZyIiIi1GJjYjIiNTISIiKiYtJSZGbG9hdEc2JCIlUyYqISIjRiwlIiVHRiw=

binF(100,0.5,60)-binF(100,0.5,40);

NiMkIitKJGYmUiYqISM1

(b) Normalverteilung NiMtJSJORzYkJSNtdUcqJCklJnNpZ21hRyIiIyIiIg== wobei NiMvJSNtdUcqJiUibkciIiIlInBHRic= = 50 und NiMvKiQpJSZzaWdtYUciIiMiIiIqKCUibkdGKCUicEdGKCwmRitGKEYoISIiRig= = 25

Gesuchte Wahrscheinlichkeit: P( 41 <= X <= 60 ) = NiMvLCYtJiUiRkc2IyUiTkc2IyIjZyIiIi1GJjYjIiNUISIiKiYtJSZGbG9hdEc2JCIlOCUqISIjRiwlIiVHRiw=

1.3 % Abweichung gegen Binomialverteilung =>

Korrektur mit halben Werten notwendig wegen Ort der Histogrammgrenze

Gesuchte Wahrscheinlichkeit: P( 40.5 <= X <= 60.5 ) = NiMvLCYtJiUiRkc2IyUiTkc2Iy0lJkZsb2F0RzYkIiQwJyEiIiIiIi1GJjYjLUYsNiQiJDAlRi9GLyomLUYsNiQiJU0mKiEiI0YwJSIlR0Yw

norF(50,5,60)-norF(50,5,41);

NiMkIismWyY+OCUqISM1

norF(50,5,60.5)-norF(50,5,40.5);

NiMkIiskPiE+TSYqISM1

<Text-field layout="Heading 2" style="Heading 2">Aufgabe 5</Text-field>

restart;

n:=4040;

NiM+SSJuRzYiIiVTUw==

p:=1/2;

NiM+SSJwRzYiIyIiIiIiIw==

1 - binF(4040,0.5, 2047);

NiMkIislM2FWJD4hIzU=

a:=n*p;

NiM+SSJhRzYiIiU/Pw==

sig2:=n*p*(1-p);

NiM+SSVzaWcyRzYiIiU1NQ==

sig:=sqrt(sig2);

NiM+SSRzaWdHNiIqJCIlNTUjIiIiIiIj

1 - norF(2020,sig,2047.5);

NiMkIitvPE1NPiEjNQ==

1 - norF(2020,sig,2048);

NiMkIitDOVoiKj0hIzU=