7. Dolphin behavior (seen in HW5). The behavior of dolphins in the presence of tour boats inPatagonia, Argentina is studied in Dans et al. (2012). A Markov chain model is developed, withstate 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 0.040.03 0.80 0.04 0.10 0.03P = | 0.01 0.15 0.70 0.07 0.070.03 0.19 0.02 0.75 0.01\0.03 0.09 0.050.83/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-terma.

Answered: - Dolphin behavior (seen in HW5). The…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A continuous-time Markov chain (CTMC) has the following Q= (gij) matrix (all rates are transition/second) O 29 48 41 3 18 21 Q = (dij) 9. 19 13 6 22 8 Given that the process is in state 1, the probability to move next to state 2 or 3 is 00.34746 00.66667 00.53472 0.65254
Aileen, a Scottish spy, has three fake identities that she uses to get information. The process is really quite involved, but she uses a Markov chain process to make it more difficult for her Irish adversaries to track her: "Hope" (state 1), "Trixie"(state 2), and "Fiona" (state 3). The transition matrix is .5 .5 P = .2 .2 .6 .4 .1 .5 On the first observation, Aileen used "Trixie" as her identity. Which of the three fake identities is she most likely to have used on the third observation? O Hope and Fiona are equally likely O Hope and Trixie are equally likely Fiona О Норе O None of the others are correct O Trixie
An intelligent irigation system supplies the amount of water (small or large) to crops in a daily basis based on the observation of surrounding temperature (hot or cold) and the condition of the soil (wet or dry). Nevertheless, it is found that the soil condition significantly impacts the decision compared to the surrounding temperature. Using Hidden Markov Model and considering only the amount of water and the soil condition, answer the following questions. i. Identify the states, observations and all the related probabilities. Then, create a graphical model to show the connection between the staté and observation sequence. i. Calculate a probability of a sequence of observations for Wet, 'Dry'}.
Long-Run Properties of Markov Chains The leading brewery on the West Coast (labeled A) has hired an OR analyst to analyze its market position. It is particularly concerned about its major competitor (labeled B). The analyst -believes that brand switching can be modeled as a Markov chain using three states, with states A and B representing customers drinking beer produced from the aforementioned breweries and state C representing all other brands. Data are taken monthly, and the analyst has constructed the following (one-step) transition -matrix from past data. What are the steady-state market shares for the two major -breweries?
A coin is tossed three times. An outcome is represented by a string of the sort HTT (meaning a head on the first toss, followed by two tails). The 8 outcomes are listed in the table below. Note that each outcome has the same probability. For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. Event A: Alternating head and tail (with either coming first) Event B: More heads than tails Event C: A tail on the first toss TTT HHH U O U TTH THT O O Outcomes O O O O HTH HTT O O O O O O THH O O HHT O O Probability X
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.)
3. (a) A Markov process with 2 states is used to model the weather in a certain town. State 1 corresponds to a suny day. State 2 corresponds to a rainy day. The transition matrix for this Markov process is [0.7 0.4] 0.3 0.6 %3D (i) If today is rainy, what is the probability that tomorrow will be sunny? (ii) Find the steady state probability vector. (iii) In the long run, how many days a week are sunny?
Cs401 3b
Find the vector of stable probabilities for the Markov chain whose transition matrix is
5

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