pro prob9_2,n,dz=dz

aobs=40.
bobs=20.

  
dr=0.5
if not keyword_set(dz) then dz=1.
z0=6.

err1a=randomn(seed,n)*dr
err1b=randomn(seed,n)*dr
err2=randomn(seed,n)*dz+z0

apran=aobs+err1a-err2
bpran=bobs+err1b-err2
print,'mean(ap)=',mean(apran),' mean(bp)=',mean(bpran)

ap=aobs-z0
bp=bobs-z0
rat=apran/bpran

da=sqrt(dr^2+dz^2)
db=da

print,'mean ratio   (analytic (1st order) vs. sampling)',ap/bp, mean(rat)
print,'mean ratio (analyt. + cov + var(b) vs. sampling)',ap/bp-1./bp^2*dz^2+ap/bp^3*db^2, mean(rat)

df1_2=(da/bp)^2+(db*ap/bp^2)^2
df_2=df1_2-2.*dz^2*ap/bp^3

print,'errors on ratio (analytic vs. sampling)',sqrt(df_2), stdev(rat)

print
print,'now different systematic errors (= without covariance)'
print

err2a=randomn(seed,n)*dz+z0
bpran=bobs+err1b-err2a
print,'mean(ap)=',mean(apran),' mean(bp)=',mean(bpran)

rat=apran/bpran

print,'mean ratio   (analytic (1st order) vs. sampling)',ap/bp, mean(rat)
print,'mean ratio   (analytic + var(b)    vs. sampling)',ap/bp+ap/bp^3*db^2, mean(rat)
print,'errors on ratio (analytic vs. sampling)',sqrt(df1_2), stdev(rat)

return
end