问题

Let $X$ denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters(從出生地移動到它遇到的第一個領土空缺). 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 $100$ m? At most $200$ m? Between $100$ and $200$ m?
• (b) What is the probability that distance exceeds the mean distance by more than $2$ standard deviation?
• (c) What is the value of the median distance?