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<Worksheet><Version major="6" minor="0"/><View-Properties><Hide name="Section Range"/><Zoom percentage="100"/></View-Properties><Styles><Layout alignment="left" bullet="none" name="Heading 3" spaceabove="0.0" spacebelow="0.0"/><Layout alignment="left" bullet="none" name="Heading 2" spaceabove="8.0" spacebelow="2.0"/><Layout alignment="left" bullet="none" name="Heading 1" spaceabove="8.0" spacebelow="4.0"/><Layout alignment="left" bullet="none" firstindent="0.0" leftmargin="0.0" linebreak="space" name="Normal" rightmargin="0.0" spaceabove="0.0" spacebelow="0.0"/><Layout alignment="centred" bullet="none" name="Maple Plot"/><Layout alignment="centred" bullet="none" linespacing="0.5" name="Maple Output"/><Font background="[0,0,0]" bold="true" family="Serif" italic="true" name="Heading 3" opaque="false" size="14"/><Font background="[0,0,0]" bold="true" family="Serif" name="Heading 2" opaque="false" size="16"/><Font background="[0,0,0]" bold="true" family="Serif" name="Heading 1" opaque="false" size="18"/><Font background="[0,0,0]" family="Lucida Bright" foreground="[0,0,255]" name="2D Output" opaque="false" readonly="true" size="12"/><Font background="[0,0,0]" bold="true" executable="true" family="Monospaced" foreground="[255,0,0]" name="Maple Input" opaque="false" size="12"/></Styles><Section><Title><Text-field layout="Heading 1" style="Heading 1">Pruefung 1</Text-field></Title><Section collapsed="true"><Title><Text-field layout="Heading 2" style="Heading 2">Aufgabe 1</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">restart;</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">K:=200*0.15;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSJLRzYiJCIlK0khIiM=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">hyper:=(N,K,n,k)-&gt;evalf((binomial(K,k)*binomial(N-K,n-k))/binomial(N,n));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSZoeXBlckc2ImYqNiZJIk5HRiVJIktHRiVJIm5HRiVJImtHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJS1JJmV2YWxmR0kqcHJvdGVjdGVkR0YxNiMqKC1JKWJpbm9taWFsR0YlNiQ5JTknIiIiLUY1NiQsJjkkRjlGNyEiIiwmOSZGOUY4Rj5GOS1GNTYkRj1GQEY+RiVGJUYl</Equation></Text-field></Output></Group><Section><Title><Text-field layout="Heading 3" style="Heading 3">a)</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">100*hyper(200,30,20,5);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIisnW1lNLSIhIik=</Equation></Text-field></Output></Group></Section><Section><Title><Text-field layout="Heading 3" style="Heading 3">b)</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">100*(1-sum(hyper(200,30,20,i),i=0..11));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIiU0JSkhIik=</Equation></Text-field></Output></Group></Section><Section><Title><Text-field layout="Heading 3" style="Heading 3">c)</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">100*(sum(hyper(200,30,20,i),i=0..4));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIisqXFheUykhIik=</Equation></Text-field></Output></Group></Section><Section><Title><Text-field layout="Heading 3" style="Heading 3">d)</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">Tardy:= (x) -&gt; evalf(product((170-i)/(200-i), i=0..x-1));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSZUYXJkeUc2ImYqNiNJInhHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJS1JJmV2YWxmR0kqcHJvdGVjdGVkR0YuNiMtSShwcm9kdWN0RzYkRi5JKF9zeXNsaWJHRiU2JComLCYiJHEiIiIiSSJpR0YlISIiRjgsJiIkKyNGOEY5RjpGOi9GOTsiIiEsJjkkRjhGOkY4RiVGJUYl</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">100*Tardy(20);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIitXS3NOSyEiKg==</Equation></Text-field></Output></Group></Section></Section><Section collapsed="true"><Title><Text-field layout="Heading 2" style="Heading 2">Aufgabe 2</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">restart;</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">binom:=(n,p,k)-&gt;binomial(n,k)*p^k*(1-p)^(n-k);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSZiaW5vbUc2ImYqNiVJIm5HRiVJInBHRiVJImtHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSooLUkpYmlub21pYWxHRiU2JDkkOSYiIiIpOSVGM0Y0KSwmRjRGNEY2ISIiLCZGMkY0RjNGOUY0RiVGJUYl</Equation></Text-field></Output></Group><Section><Title><Text-field layout="Heading 3" style="Heading 3">a)</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">100*binom(250,0.39,100);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIitaIzRCKVshIio=</Equation></Text-field></Output></Group></Section><Section><Title><Text-field layout="Heading 3" style="Heading 3">b)</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">100*(sum(binom(250,0.39,i),i=0..225));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIisrKysrNSEiKA==</Equation></Text-field></Output></Group></Section><Section><Title><Text-field layout="Heading 3" style="Heading 3">c)</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">plot(binom(250,0.39,x), x=97..98);</Text-field></Input><Output><Text-field layout="Maple Plot"><Plot height="400" type="two-dimensional" width="400">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</Plot></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">100*binom(250,0.39,97);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIitTRlZoXiEiKg==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">100*binom(250,0.39,98);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIishSE4+OiYhIio=</Equation></Text-field></Output></Group></Section></Section><Section collapsed="true"><Title><Text-field layout="Heading 2" style="Heading 2">Aufgabe 3</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">restart;</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">lambda:=1000/60;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSdsYW1iZGFHNiIjIiNdIiIk</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">pois:=(lambda,k)-&gt;evalf(exp(-lambda)*(lambda^k/k!));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSVwb2lzRzYiZio2JEknbGFtYmRhR0YlSSJrR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUtSSZldmFsZkdJKnByb3RlY3RlZEdGLzYjKigtSSRleHBHRiU2IywkOSQhIiIiIiIpRjY5JUY4LUkqZmFjdG9yaWFsR0YvNiNGOkY3RiVGJUYl</Equation></Text-field></Output></Group><Section><Title><Text-field layout="Heading 3" style="Heading 3">a)</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">100*pois(lambda,20);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIiskW1lhXCchIio=</Equation></Text-field></Output></Group></Section><Section><Title><Text-field layout="Heading 3" style="Heading 3">b)</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">100*(sum(pois(lambda,i),i=0..19));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIisrZSYpR3chIik=</Equation></Text-field></Output></Group></Section><Section><Title><Text-field layout="Heading 3" style="Heading 3">c)</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">100*(1-sum(pois(lambda,i),i=0..30));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIilLd3M1ISIp</Equation></Text-field></Output></Group></Section></Section><Section collapsed="true"><Title><Text-field layout="Heading 2" style="Heading 2">Aufgabe 4</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">restart;</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">binom:=(n,p,k)-&gt;evalf(binomial(n,k)*p^k*(1-p)^(n-k));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSZiaW5vbUc2ImYqNiVJIm5HRiVJInBHRiVJImtHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJS1JJmV2YWxmR0kqcHJvdGVjdGVkR0YwNiMqKC1JKWJpbm9taWFsR0YlNiQ5JDkmIiIiKTklRjdGOCksJkY4RjhGOiEiIiwmRjZGOEY3Rj1GOEYlRiVGJQ==</Equation></Text-field></Output></Group><Section><Title><Text-field layout="Heading 3" style="Heading 3">a)</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">100*binom(150,11/210,10);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIit6SEpRKCohIio=</Equation></Text-field></Output></Group></Section><Section><Title><Text-field layout="Heading 3" style="Heading 3">b)</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">p:=18/210+19/210+20/210;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSJwRzYiIyIjPiIjcQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">100*binom(150,p,33);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIis2dHhcRiEiKg==</Equation></Text-field></Output></Group></Section><Section><Title><Text-field layout="Heading 3" style="Heading 3">c)</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">p:=1/210+3/210+5/210+7/210+11/210+13/210+17/210+19/210;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSJwRzYiIyIjUSIkMCI=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">100*binom(150,p,43);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIitTLCkqcDUhIio=</Equation></Text-field></Output></Group></Section><Section><Title><Text-field layout="Heading 3" style="Heading 3">d)</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">sum(i/210,i=1..20);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMiIiI=</Equation></Text-field></Output></Group></Section></Section><Section collapsed="true"><Title><Text-field layout="Heading 2" style="Heading 2">Aufgabe 5</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">restart;</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">jahr:=24*365;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSVqYWhyRzYiIiVnKCk=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">ausfall_h:=evalf(8*10^(-4)*jahr/1000);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSphdXNmYWxsX2hHNiIkIisrKyszcSEjNw==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">ausfall:=100/jahr*ausfall_h;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SShhdXNmYWxsRzYiJCIrKysrKyEpISM5</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">verfuegbar:=100-ausfall;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSt2ZXJmdWVnYmFyRzYiJCIrKz8qKioqKiohIik=</Equation></Text-field></Output></Group></Section><Section collapsed="true"><Title><Text-field layout="Heading 2" style="Heading 2">Aufgabe 6</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">restart;</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">binom:=(n,p,k)-&gt;evalf(binomial(n,k)*p^k*(1-p)^(n-k));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSZiaW5vbUc2ImYqNiVJIm5HRiVJInBHRiVJImtHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJS1JJmV2YWxmR0kqcHJvdGVjdGVkR0YwNiMqKC1JKWJpbm9taWFsR0YlNiQ5JDkmIiIiKTklRjdGOCksJkY4RjhGOiEiIiwmRjZGOEY3Rj1GOEYlRiVGJQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">100*(1-binom(500,1/365,0));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIitpYk5qdSEiKQ==</Equation></Text-field></Output></Group></Section></Section><Text-field/><Text-field/><Text-field/><Text-field/><Text-field/></Worksheet>