%stat351_introduction5.m
% run tests

>>X=[ 1 1 0 1 1 1 0 0 1 1]
X =

     1     1     0     1     1     1     0     0     1     1

%Probability of gettig 3 runs of type 1 in our example
>>nchoosek(7-1,3-1)*nchoosek(3+1,3)/nchoosek(10,7)

ans =

    0.5000
    

%Iteration: For-loop
>>P=zeros(1,10)

P =

     0     0     0     0     0     0     0     0     0     0

>>for i=1:10
    P(i)=i;
end;
>>P
P =

     1     2     3     4     5     6     7     8     9    10

>>for i=1:2:10
    i
end;

i =

     1


i =

     3


i =

     5


i =

     7


i =

     9

>>mod(P,2)
ans =

     1     0     1     0     1     0     1     0     1     0
%Test if the above binary sequence is random

%Example on p.72
n1=5;
n2=4;
n=n1+n2;

>>P=zeros(1,n);
>>for r=2:2:n
  P(r)=2*nchoosek(n1-1,r/2-1)*nchoosek(n2-1,r/2-1)/nchoosek(n,n1);
end;
>>for r=3:2:n
  P(r)=(nchoosek(n1-1,(r-1)/2)*nchoosek(n2-1,(r-3)/2)+ nchoosek(n1-1,(r-3)/2)...
       *nchoosek(n2-1,(r-1)/2))/nchoosek(n,n1);
end;

%You will get error message
??? Error using ==> nchoosek
K must be an integer between 0 and N

>> P'

ans =

         0
    0.0159
    0.0556
    0.1905
    0.2381
    0.2857
    0.1429
    0.0635
         0
>>sum(P)
ans =

    0.9921

>>r=9
>>P(r)=nchoosek(n1-1,(r-1)/2)*nchoosek(n2-1,(r-3)/2)/nchoosek(n,n1);
>>P'

ans =

    1.0000
    
>> P'
ans =

         0
    0.0159
    0.0556
    0.1905
    0.2381
    0.2857
    0.1429
    0.0635
    0.0079
%At 5% level reject if r <=2 or r >=9