Reconsider Prob. 22.6-4.

Suppose now that more careful statistical analysis has provided new estimates of the probability distributions of the radii of the shafts and bushings. In actuality, the probability distribution of the radius of a shaft (in inches)

has the probability density function fs(x) 

Similarly, the probability distribution of the radius of a bushing (in inches) has the probability density function fB(x) 

Obtaining uniform random numbers as instructed at the beginning of the Problems section, perform a simulated experiment for estimating the probability of interference. Notice that almost all cases of interference will occur when the radius of the bushing is much closer to 1.0000 inch than to 1.0100 inches. Therefore, it appears that an efficient experiment would generate most of the simulated bushings from this critical portion of the distribution.

Take this observation into account in part (b). For each of the following cases, use the same 10 pairs of uniform random numbers to generate random observations, and calculate the resulting estimate of the probability of interference.

(a) Use the crude Monte Carlo technique.

(b) Develop and apply a stratified sampling approach to this problem.

(c) Use the method of complementary random numbers.