Circuit breaker Use the data from Problem 3.4 and the results from Problem 9.7. Compare the two samples of size 18 from the new design using the likelihood ratio test, as follows. Use a computer program, if available
(a) Assume that both samples come from the same exponential distribution with (unknown) true mean
Write the sample log likelihood 
for the combined samples.
(b) Calculate the ML estimate 
for the assumed common exponential distribution and the corresponding maximum log likelihood
(c) Assume that the sample with failures comes from an exponential distribution with unknown true mean 
and the other sample ha a true other proportion π0 failed by 15,000 cycles. (There is no need to assume that the distribution is exponential.) Write the sample log likelihood 
for the two samples.
(d) Calculate the ML estimates 
and 
and the corresponding maximum log likelihood.
(e) Calculate the log likelihood ratio test statistic. How many degrees of freedom does it have? Do the samples differ statistically significantly?
( f ) In your opinion, is the asymptotic theory crude or adequate for is the asymptotic theory crude or adequate for these samples? Explain.