et X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter x=0.1386 (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 100m? At most 200m?Between 100 and 200m? 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?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter x=0.1386 (as suggested in the article “Competition and Dispersal from Multiple Nests,” Ecology, 1997:873–883).
a.What is the
b.What is the probability that distance exceeds the mean distance by more than 2 standard deviations?
c.What is the value of the
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