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p=[.1 .1 .2 (.25-1) .35];
min(roots(p))


              Exercises/Experiments
2.
p=.7; q=0; r=.3;
x=(p+q/2)^2 
y=2*(p+q/2)*(r+q/2) 
z=(r+q/2)^2
X=(x+y/2)^2
Y=2*(x+y/2)*(z+y/2)
Z=(z+y/2)^2

3c.
for part(b):
pa=(.001:.001:.25);
pA=1-pa;
u=(2*pA.*pa).^2*(1/4)+2*(2*pA.*pa).*pa.^2*(1/2)+(pa.^2).^2;
aaxaa=pa.^4./u;
plot(pa,aaxaa)

for part(c):
k=10; pa(k) % so pa(10)=0.01
aaxaa(k)

4d.
T=[0 1; .5 .5]
x=[1 0]
for k=1:20
x=x*T
end
y=x  % print eigenvector
lambda = y(1)/x(1) % and evalue

6.
c=1/3; P(1)=.7;
p=.8
for k=1:30
 P(k+1)=c*P(k)+(1-c)*p^2;
end
P
c=.9;
for k=1:30
 P(k+1)=c*P(k)+(1-c)*p^2;
end
P % how does P(infinity) depend on c?
p=.3
for k=1:50
 P(k+1)=c*P(k)+(1-c)*p^2;
end
P % compare P(infinity) with p^2