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Probability with Applications in Engineering, Science, and Technology
Let $X$ denote the distance $(\mathrm{m})$ that an animal moves from its site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, $X$ has an exponential distribution with parameter $\lambda=.01386$ (as suggested in the article "Competition and Dispersal from Multiple Nests," Ecology, $1997 : 873-883$ ).
(a) What is the probability that the distance is at most 100 $\mathrm{m}$ ? At most 200 $\mathrm{m}$ ? Between 100 and 200 $\mathrm{m} ?$
(b) What is the probability that distance exceeds the mean distance by more than 2 standard deviations?
(c) What is the value of the median distance?