5.6 Consider a Poisson variable X of mean .

(a) We want to set 90% confidence upper limits to the value of the parent mean

, assuming that one measurement of the variable yielded the result of N D 1.

Following the classical approach, find the equation that determines the exact 90% upper limit to the mean up. Recall that the classical 90% confidence upper limit is defined as the value of the Poisson mean that yields a P.X N/ D ˇ, where 1  ˇ D 0:9.

(b) Using the Bayesian approach, which consists of defining the 1ˇ D 0:9 upper limit via ˇ D R up 0 P.nobs=/d
R 1 0 P.nobs=/d
(5.32)
where nobs D N; find the equation that determines the 90% upper limit to the mean up.