- Dolphin behavior (seen in HW5). The behavior of dolphins in the presence of tour boats in Patagonia, Argentina is studied in Dans et al. (2012). A Markov chain model is developed, with state space consisting of five primary dolphin activities (socializing, traveling, milling, feeding, and resting). The following transition matrix is obtained. (0.84 0.11 0.01 0.04 0.03 0.80 0.04 0.10 0.03 P = 0.01 0.15 0.70 0.07 0.07 0.03 0.19 0.02 0.75 0.01 \0.03 0.09 0.05 0.83/ Use technology to find the long-term distribution of dolphin activity. b. using this result, predict what behavior is the most likely to be observe long-term a.

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Find the steady state matrix X of the absorbing Markov chain with matrix of transition probabilities P. 0.4 0 0.3 1 0.6 0 0.1 X = P = 0.3 0.3 000

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In an office complex of 1000 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 85% chance that she will be at work tomorrow, and if the employee is absent today, there is a 70% chance that she will be absent tomorrow. Suppose that today there are 740 employees at work. (A graphing calculator is recommended.) (a) Find the transition matrix A for this scenario. at work absent A = (b) Predict the number that will be at work five days from now. (Round your answer to the nearest integer.) employees (c) Find the steady-state vector x. (Round your answer to two decimal places.)

A Markov chain model for a species has four states: State 0 (Lower Risk), State 1 (Vulnerable), State 2 (Threatened), and State 3 (Extinct). For t 2 0, you are given that: 01 zit = 0.03 12 t= 0.05 23 Hit = 0.06 This species is currently in state 0. Calculate the probability this species will be in state 2 ten years later. Assume that reentry is not possible. (Note: This question is similar to #46.2 but with constant forces of mortality) Possīble Answers A 0.02 0.03 0.04 D 0.05 E 0.06