4.) Ecology: River Otters A doctoral thesis published in 1982 studied the social

Question

4.) Ecology: River Otters A doctoral thesis published in 1982 studied the social behavior of river otters during the mating season. An important role in the bonding process of river otters is very short periods of social grooming. After extensive observations, the researcher found that one group of river otters under study hada frequency of initiating grooming of approximately 1.7 for each 10 minutes. Suppose that you are observing nver otters for 30 minutes. Let r = 1,2, be a random variable that represents the number of times (in a 30-minute interval) one otter initiates social grooming of another. a) Explain why the Poisson distribution would be a good choice for the probability distribution of r. b) What is the expected value of the number of groomings initiated in a 30- minute period? c) Write out the formula for the probability distribution of the random variable

Explanation / Answer

(a) If a mean or average probability of an event happening per unit time/per page/per mile cycled etc., is given, and you are asked to calculate a probability of n events happening in a given time/number of pages/number of miles cycled, then the Poisson Distribution is used. Here we shall use poisson probability distribution as here we know the rate of grooming per 10 miutes for otters.

(b) Expected number of groomings = (30/20) * 1.7 = 5.1

(c) Pr(r) = POISSON (r, n) = e-5.1 5.1r/r!

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