At time t = 0, 19 identical components are tested. the lifetime distribution of each is exponential with parameter λ. the experimenter then leaves the test facility unmonitored. on his return 24 hours later, the experimenter immediately terminates the test after noticing that y = 13 of the 19 components are still in operation (so 6 have failed). derive the mle of λ. [hint: let y = the number that survive 24 hours. then y ~ bin(n, p). what is the mle of p? now notice that p = p(xi ≥ 24), where xi is exponentially distributed. this relates λ to p, so the former can be estimated once the latter has been.] (round your answer to four decimal places.)

Questions 9-10. use the table of educational expenditures to answer the questions. k-12 education expenditures population indiana $9.97 billion 6.6 million illinois $28.54 billion 12.9 million kentucky $6.58 billion 4.4 million michigan $16.85 billion 9.9 million ohio $20.23 billion 11.6million 9. if the amount of k-12 education expenses in indiana were proportional to those in ohio, what would have been the expected value of k-12 expenditures in indiana? (give the answer in billions rounded to the nearest hundredth) 10. use the value of k-12 education expenditures in michigan as a proportion of the population in michigan to estimate what the value of k-12 education expenses would be in illinois. a) find the expected value of k-12 expenditures in illinois if illinois were proportional to michigan. (give the answer in billions rounded to the nearest hundredth) b) how does this compare to the actual value for k-12 expenditures in illinois? (lower, higher, same? )