%problem 1
disp('(1)');
beta=-2:0.5:2;
pr=1+normcdf(-1.645-beta)-normcdf(1.645-beta);
disp([beta;pr]);
%problem 2
%(b)
disp('(2a)');
MAX=100000;
beta=[-1 -1 -1  0  0  0  1  1  1
       1  0 -1  1  0 -1  1  0  -1];
r=0.6;  C=[sqrt(1-r*r) r; 0 1];
pra=zeros(1,9);
for j=1:9
    for i=1:MAX
        z=randn(2,1);
        b=beta(:,j)+C*z;
        W0=b'*inv(C*C')*b;
        if W0>5.99
            pra(j)=pra(j)+1;
        end
    end
end
pra=pra/MAX;
disp([beta; pra]);
disp('(2b)');
r=-0.6;  C=[sqrt(1-r*r) r; 0 1];
prb=zeros(1,9);
for j=1:9
    for i=1:MAX
        z=randn(2,1);        
        b=beta(:,j)+C*z;            
        W0=b'*inv(C*C')*b;
        if W0>5.99
            prb(j)=prb(j)+1;
        end
    end
end
prb=prb/MAX;
disp([beta; prb]);