290 Chapter 7: Parameter Estimation
If the average life of the first 20 chips tested is 4.6 hours, compute the Bayes
estimate ofλ.
64.Each item produced will, independently, be defective with probabilityp. If the
prior distribution onpis uniform on (0, 1), compute the posterior probability
thatpis less than .2 given
(a) a total of 2 defectives out of a sample of size 10;
(b) a total of 1 defective out of a sample of size 10;
(c) a total of 10 defectives out of a sample of size 10.
65.The breaking strength of a certain type of cloth is to be measured for 10 spec-
imens. The underlying distribution is normal with unknown meanθbut with
a standard deviation equal to 3 psi. Suppose also that based on previous experience
we feel that the unknown mean has a prior distribution that is normally dis-
tributed with mean 200 and standard deviation 2. If the average breaking strength
of a sample of 20 specimens is 182 psi, determine a region that containsθwith
probability .95.