A hole is drilled into the Antarctic ice shelf and a core is extracted that provides information on the climate when the ice was formed at different times in the past. Suppose that a researcher is interested in high-temperature years, and that the places in the core corresponding to high-temperature years occur according to a Poisson process with parameter X = 0.48 per cm.
(a) What is the expected distance in cm between adjacent high-temperature years?
(b) What is the expected distance in cm between one high-temperature year and the 10th high-temperature year that followed after it?
(c) What is the probability that the distance between two adjacent high-temperature years is less that 0.5 cm?
(d) Suppose that a 20-cm section of core is analyzed. What is the probability that the number of high-temperature years in this section of core is between 8 and 12 inclusive.'