Page 54

```Matlab: Roulette Wheel Selection, Breakpoint Method

% set up the outcomes
oc(1)=2; oc(2)=3; oc(3)=4; oc(4)=5;
% set up the breakpoints
bp(1)=.15; bp(2)=bp(1)+.2; bp(3)=bp(2)+.60; bp(4)=1;
% end of set up, go here to get samples
U=rand; k=1;
while( U >= bp(k))
k=k+1;
end % k is selected
selected = oc(k)
```

Page 55

```Matlab: Roulette Wheel Selection, Density Method

i=1;
for j=1:15
oc(i)=2; i=i+1;
end;
for j=1:20
oc(i)=3; i=i+1;
end;
for j=1:60
oc(i)=4; i=i+1;
end;
for j=1:5
oc(i)=5; i=i+1;
end;
% end of setup, go here to get samples
k=floor(100*rand)+1;
selected = oc(k)
```

Page 55

```Matlab: Roulette Wheel Selection, Vector Method

b(1)=.15; b(2)=b(1)+.2; b(3)=b(2)+.6;
U=rand(1,10000); %10000 U(0,1) samples
w2 = (U < b(1))*2;
w3 = (U >=b(1) & U < b(2))*3;
w4 = (U >=b(2) & U < b(3))*4;
w5 = (U >=b(3))*5;
w=w2+w3+w4+w5; % w a random 10000 vector
% with the right frequencies
```

Page 73

```Matlab: Normal CDF via Rational Approximation

function w = normalCDF(x)
a1 = 0.31938153; a2 = -0.356563782;
a3 = 1.781477937; a4 = -1.821255978;
a5 = 1.330274429; b=0.2316410; c=1/sqrt(2*pi);
L=abs(x); K=1./(1+b.*L);
w = 1-c*exp(-L.*L/2).*...
(a1.*K+a2.*K.^2+a3.*K.^3+a4.*K.^4+a5.*K.^5);
msign = -(x <0); mfact = 2*msign+1;
w = mfact.*(w+msign);
```