A professor has two light bulbs in his garage. When both are burned out, they are replaced, and the next day starts with two working light bulbs. Supposethat when both are working, one of the two will go out with probability 0.02 (eachhas probability 0.01 and we ignore the possibility of losing two on the same day).However, when only one is there, it will burn out with probability 0.05. (i) What isthe long-run fraction of time that there is exactly one bulb working? (ii) What is theexpected time between light bulb replacements?

Farmers know that driving heavy equipment on wet soil compresses the soil and injures future crops. here are data on the "penetrability" of the same type of soil at two levels of compression. penetrability is a measure of how much resistance plant roots will meet when they try to grow through the soil. compressed soil 2.85 2.66 3 2.82 2.76 2.81 2.78 3.08 2.94 2.86 3.08 2.82 2.78 2.98 3.00 2.78 2.96 2.90 3.18 3.16 intermediate soil 3.17 3.37 3.1 3.40 3.38 3.14 3.18 3.26 2.96 3.02 3.54 3.36 3.18 3.12 3.86 2.92 3.46 3.44 3.62 4.26 use the data, omitting the high outlier, to give a 95% confidence interval for the decrease in penetrability of compressed soil relative to intermediate soil. compute degrees of freedom using the conservative method. interval: to