proc iml; sum=0; do i=1 to 11; sum=sum+(i**2/(i+1))-2*i; end; print 'Problem 1:' sum; prod=1; do i=6 to 10; prod=prod*(i+1)/(i+2); end; print 'Problem 2:' prod; theta=4.5; sum=0; do i=0 to 9; if i=0 then prod=1; if i>0 then do; prod=1; do j=1 to i; prod=prod*j; end; end; sum=sum+theta**i/prod; end; prob=sum*exp(-theta); print 'Problem 3a:' prob; sum=0; do i=0 to 4; if i=0 then prod=1; if i>0 then do; prod=1; do j=1 to i; prod=prod*j; end; end; sum=sum+theta**i/prod; end; prob=1-sum*exp(-theta); print 'Problem 3b:' prob; n=20; seed=398389; c=j(n,1,seed); z=normal(c); mean=z[+]/n; sd=sqrt(z`*(i(n)-(1/(n-1))*j(20,20,1))*z/(n-1)); print 'Problem 4:' mean sd; n=20; seed2=54278; c2=j(n,1,seed2); z2=normal(c2); mu=10; sig2=2; y=mu*j(n,1,1)+sqrt(sig2)*z2; mean=y[+]/n; sd=sqrt(y`*(i(n)-(1/n)*j(n,n,1))*y/(n-1)); print 'Problem 5:' mean sd; m=10; do i=1 to m; seed2=54278; c2=j(n,1,seed2); z2=normal(c2); mu=10; sig2=2; y=mu*j(n,1,1)+sqrt(sig2)*z2; mean1=mean1//y[+]/n; sd1=sd1//sqrt(y`*(i(n)-(1/n)*j(n,n,1))*y/(n-1)); end; m_mean=mean1[+]/m; se1_mean=sd1[+]/m; se2_mean=sqrt(mean1`*(i(m)-(1/m)*j(m,m,1))*mean1/(m-1)); *print mean1; se_true=sqrt(sig2/m); print 'Problem 6:' mean1 sd1 m_mean se1_mean se2_mean se_true;