<?xml version="1.0" encoding="UTF-8"?>
<Worksheet><Version major="6" minor="0"/><View-Properties><Zoom percentage="100"/></View-Properties><Styles><Layout alignment="left" bullet="none" name="Warning"/><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]" family="Monospaced" foreground="[0,0,255]" name="Warning" opaque="false" readonly="true" size="12"/><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">Uebung 9</Text-field></Title><Section collapsed="true"><Title><Text-field layout="Heading 2" style="Heading 2">Funktionen</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false"># binf, binF: Binomialverteilung<Font encoding="ISO8859-1">
#             Z\344hldichte b(n,p;k), V-Funktion F(n,p;k)</Font></Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">binf := proc(n,p,k)
   return evalf( binomial(n,k)*p^k*(1-p)^(n-k) );
end proc:</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">binF := proc(n,p,k)
   local i;
   return evalf( sum(binf(n,p,i),i=0..k) );
end proc:</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"/></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false"># hypf, hypF: Hypergeometrische Verteilung<Font encoding="ISO8859-1">
#             Z\344hldichte h(N,K,n;k), V-Funktion F(N,K,n;k)</Font></Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">hypf := proc(N,K,n,k)
   return evalf( binomial(K,k)*binomial(N-K,n-k)/binomial(N,n) );
end proc:</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">hypF := proc(N,K,n,k)
   local i;
   return evalf( sum(hypf(N,K,n,i),i=0..k) );
end proc:</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"/></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false"># poif, poiF: Poisson-Verteilung<Font encoding="ISO8859-1">
#             Z\344hldichte pi(lambda;k), V-Funktion F(lambda;k)</Font></Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">poif := proc(la,k)
   return evalf( exp(-la)*la^k/k! );
end proc:</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">poiF := proc(la,k)
   local i;
   return evalf( sum(poif(la,i),i=0..k) );
end proc:</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"/></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false"># norf, norF: Normalverteilung
#             Dichtefunktion f(a,sig;x), v-Funktion F(a,sig;x)</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">norf := (a,sig,x) -&gt; evalf(1/(sig*sqrt(2*Pi)))*exp((-1/2)*((x-a)/sig)^2):</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">norF := (a,sig,x) -&gt; evalf( int(norf(a,sig,t),t=-infinity..x)):</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"/></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">mittelwert := proc(l)
	return sum(l[i],i=1..nops(l))/nops(l);
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">varStich := proc(l)
	local m;
	m := mittelwert(l);
	return 1/nops(l)*sum((l[i]-m)^2,i=1..nops(l));
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">varGesamt := proc(l)
	local m;
	m := mittelwert(l);
	return 1/(nops(l)-1)*sum((l[i]-m)^2,i=1..nops(l));
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"/></Input></Group></Section><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">fx:=(x)-&gt;(x+1)/4;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNmeEc2ImYqNiNJInhHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwmOSQjIiIiIiIlRi5GL0YlRiVGJQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">fy:=(y)-&gt;y+1/2;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNmeUc2ImYqNiNJInlHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwmOSQiIiIjRi4iIiNGLkYlRiVGJQ==</Equation></Text-field></Output></Group><Section collapsed="true"><Title><Text-field layout="Heading 3" style="Heading 3">a)</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">int(fx(t),t=0..2);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMiIiI=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">int(fy(t),t=0..1);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMiIiI=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"># gueltige Dichtefunktionen!!!</Text-field></Input></Group></Section><Section collapsed="true"><Title><Text-field layout="Heading 3" style="Heading 3">b)</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">fxy:=(x,y)-&gt;fx(x)*fy(y);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSRmeHlHNiJmKjYkSSJ4R0YlSSJ5R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUqJi1JI2Z4R0YlNiM5JCIiIi1JI2Z5R0YlNiM5JUYyRiVGJUYl</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">Fxy:=(x,y)-&gt;int(int(fx(u)*fy(v),u=0..x),v=0..y);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSRGeHlHNiJmKjYkSSJ4R0YlSSJ5R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUtSSRpbnRHNiRJKnByb3RlY3RlZEdGMEkoX3N5c2xpYkdGJTYkLUYuNiQqJi1JI2Z4R0YlNiNJInVHRiUiIiItSSNmeUdGJTYjSSJ2R0YlRjovRjk7IiIhOSQvRj47RkE5JUYlRiVGJQ==</Equation></Text-field></Output></Group></Section><Section collapsed="true"><Title><Text-field layout="Heading 3" style="Heading 3">c)</Text-field></Title><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">Fxy(7/4,3/4)-Fxy(7/4,1/4)-Fxy(1/4,3/4)+Fxy(1/4,1/4);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMjIiIkIiIp</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><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">mu:=n*p;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNtdUc2IiomSSJuR0YlIiIiSSJwR0YlRig=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">sig2:=n*p*(1-p);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSVzaWcyRzYiKihJIm5HRiUiIiJJInBHRiVGKCwmRihGKEYpISIiRig=</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">mu:=alpha;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNtdUc2IkkmYWxwaGFHRiU=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">sig2:=1/alpha^2;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSVzaWcyRzYiKiRJJmFscGhhR0YlISIj</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">fx:=(x)-&gt;(x+1)/4;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNmeEc2ImYqNiNJInhHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwmOSQjIiIiIiIlRi5GL0YlRiVGJQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">fy:=(y)-&gt;y+1/2;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNmeUc2ImYqNiNJInlHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwmOSQiIiIjRi4iIiNGLkYlRiVGJQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">muX:=<Font italic="false" underline="false">int(x*fx(x),x=0..2);</Font></Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSRtdVhHNiIjIiIoIiIn</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">sig2X:=<Font italic="false" underline="false">int((x-muX)^2*fx(x),x=0..2);</Font></Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSZzaWcyWEc2IiMiIzYiI08=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">muY:=<Font italic="false" underline="false">int(x*fy(x),x=0..1);</Font></Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSRtdVlHNiIjIiIoIiM3</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">sig2Y:=<Font italic="false" underline="false">int((x-muY)^2*fy(x),x=0..1);</Font></Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSZzaWcyWUc2IiMiIzYiJFci</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">mu2XY:=2*muX+muY;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSZtdTJYWUc2IiMiI04iIzc=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">sig22XY:=2^2*sig2X+sig2Y;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SShzaWcyMlhZRzYiIyIkKD0iJFci</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">with(plots):</Text-field></Input><Output><Text-field layout="Warning" style="Warning">Warning, the name changecoords has been redefined
</Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">with(stats):</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">with(statplots):</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">with(describe):</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">l := [8.32,8.02,8.76,8.62,7.49,7.94,8.73,8.81,8.12,8.40,8.52,8.58,8.15,8.82,7.87];</Font></Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSJsRzYiNzEkIiRLKSEiIyQiJC0pRikkIiR3KUYpJCIkaSlGKSQiJFwoRikkIiQlekYpJCIkdClGKSQiJCIpKUYpJCIkNylGKSQiJFMpRikkIiRfKUYpJCIkZSlGKSQiJDopRikkIiQjKSlGKSQiJCh5Rik=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">histogram(l,area=count,numbars=10);</Font></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">xm:=mittelwert(l);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSN4bUc2IiQiK0xMTFYkKSEiKg==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">varStichprobe:=varStich(l);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SS52YXJTdGljaHByb2JlRzYiJCIrKikpKSlbXCIhIzU=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">varGrundgesamtheit:=varGesamt(l);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+STN2YXJHcnVuZGdlc2FtdGhlaXRHNiIkIittbW0sOyEjNQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">display([plot(norf(xm,sqrt(varStichprobe),x),x=7..9),plot(norf(xm,sqrt(varGrundgesamtheit),x),x=7..9),histogram(l,area=count,numbars=10)]);</Font></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></Section><Section collapsed="true"><Title><Text-field layout="Heading 2" style="Heading 2">Aufgabe 4</Text-field></Title><Section collapsed="true"><Title><Text-field layout="Heading 3" style="Heading 3">a)</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">with(plots):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">zufall := proc()
	local rd;
	rd:=rand(0..1);
	return 2*rd()-1;
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">l:=[0];</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSJsRzYiNyMiIiE=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">for i from 1 to 1000 do
  l := [op(l), op(-1,l)+zufall()];
end do:</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">listplot(l);</Text-field></Input><Output><Text-field layout="Maple Plot"><Plot height="400" type="two-dimensional" 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collapsed="true"><Title><Text-field layout="Heading 3" style="Heading 3">b)</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">with(plots):</Text-field></Input><Output><Text-field layout="Warning" style="Warning">Warning, the name changecoords has been redefined
</Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">zufall := proc()
	local rd;
	rd:=rand(0..1);
	return 2*rd()-1;
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">l:=[[0,0]];</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSJsRzYiNyM3JCIiIUYo</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">for i from 1 to 1000 do
  l := [op(l), op(-1,l)+[zufall(),zufall()]];
end do:</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">listplot(l);</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></Section><Section collapsed="true"><Title><Text-field layout="Heading 3" style="Heading 3">c)</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">with(plots):</Text-field></Input><Output><Text-field layout="Warning" style="Warning">Warning, the name changecoords has been redefined
</Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">zufall := proc()
	local rd;
	rd:=rand(0..1000)*10^(-3);
	return evalf(2*Pi*rd());
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">l:=[[0,0]];</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSJsRzYiNyM3JCIiIUYo</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">for i from 1 to 500 do
	tmp := zufall();
	l := [op(l), [cos(tmp),sin(tmp)]];
end do:</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">listplot(l,style=point);</Text-field></Input><Output><Text-field layout="Maple Plot"><Plot height="400" type="two-dimensional" 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layout="Normal" prompt="&gt; " style="Maple Input">l:=[[0,0]];</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSJsRzYiNyM3JCIiIUYo</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">for i from 1 to 500 do
	tmp := zufall();
	l := [op(l), op(-1,l)+[cos(tmp),sin(tmp)]];
end do:</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">listplot(l);</Text-field></Input><Output><Text-field layout="Maple Plot"><Plot height="400" type="two-dimensional" 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collapsed="true"><Title><Text-field layout="Heading 3" style="Heading 3">d)</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">with(plots):</Text-field></Input><Output><Text-field layout="Warning" style="Warning">Warning, the name changecoords has been redefined
</Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">zufall := proc()
	local rd;
	rd:=rand(0..1000)*10^(-3);
	return evalf(2*Pi*rd());
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">laplace := proc(min,max)
	<Font italic="false" underline="false">return min+zufall()*(max-min)</Font>
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">l:=[[0,0]];</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSJsRzYiNyM3JCIiIUYo</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">for i from 1 to 500 do
	tmp := zufall();
	l := [op(l), [cos(tmp),sin(tmp)]];
end do:</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">listplot(l,style=point);</Text-field></Input><Output><Text-field layout="Maple Plot"><Plot height="400" type="two-dimensional" 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layout="Normal" prompt="&gt; " style="Maple Input">l:=[[0,0]];</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSJsRzYiNyM3JCIiIUYo</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">for i from 1 to 500 do
	tmp := zufall();
	a := laplace(0,100);
	l := [op(l), op(-1,l)+[a*cos(tmp),a*sin(tmp)]];
end do:</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">listplot(l);</Text-field></Input><Output><Text-field layout="Maple Plot"><Plot height="400" type="two-dimensional" 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collapsed="true"><Title><Text-field layout="Heading 3" style="Heading 3">e)</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">with(plots):</Text-field></Input><Output><Text-field layout="Warning" style="Warning">Warning, the name changecoords has been redefined
</Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">with(stats):</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">with(statplots):</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">with(describe):</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">zufall := proc()
	local rd;
	rd:=rand(0..1000)*10^(-3);
	return evalf(2*Pi*rd());
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">normalV := proc(mu,sig)<Font italic="false" underline="false">
	local tmp, rd;
	</Font>rd:=rand(0..1000)*10^(-3);<Font italic="false" underline="false">
	tmp := rd();
	return solve( norF(mu,sig,x)=tmp,x);</Font>
end proc:</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"/></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">l:=[];</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSJsRzYiNyI=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">for i from 1 to 100 do
	a := normalV(0,10);
	l := [op(l), a];
end do:</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">histogram(l,area=1,numbars=40);</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">mu:=0;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNtdUc2IiIiIQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">sig:=10;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSRzaWdHNiIiIzU=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">plot([norF(mu,sig,x),norf(mu,sig,x)],x=mu-5*sig..mu+5*sig);</Font></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"/></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">l:=[[0,0]];</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSJsRzYiNyM3JCIiIUYo</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"><Font italic="false" underline="false">for i from 1 to 500 do
	tmp := zufall();
	a := normalV(0,10);
	l := [op(l), op(-1,l)+[a*cos(tmp),a*sin(tmp)]];
end do:</Font></Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">listplot(l);</Text-field></Input><Output><Text-field layout="Maple Plot"><Plot height="400" type="two-dimensional" 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