Mary stays in her graduate student office in the basement for days, She has made up her mind notleaving her office until she completes her research project. However, she wants to know whatweather is like outside. There is a thermometer in her office, which is the only source of informationthat Mary can obtain. The following Hidden Markov Model describes the weather at day t isindependent to the weather before day t-1 given the weather at day t-1. The initial transition andsensor model is given in the following, where W is the weather outside and F is the thermometerreading.WoW;W,F1F2F3W. W-1 P(WW1)0.8FhighlowWe P(FW)Wo P(Wo)sun0.7sunsun0.9rain0.20.3sunsunsun0.3гain0.1rainrainhigh rainsun0.2rain0.7lowrain0.81. From the transition model, we can compute P(W,-sun) -0.75, P(W,-rain) =0.25. When Maryobserved F1-high, what is the probability P(W sun | F1-high)? Answer:2. From the transition model, we can compute P(W2-sun) - 0.675, P(W, rain) -0,375. But wewant to predict tomorrow's weather based on observation. What is P(W2-sun | F1-high)?Answer:3. Given P(wf1. . f) for all w, find P(W,.1|f1, . f) Answer:

Solution: From the given information,

Answered: Mary stays in her graduate student…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities. To From Special B MDA Special B 0.90 0.10 MDA 0.02 0.98 (a)Which brand appears to have the most loyal customers? Explain. MDA has the most loyal customers because ( ) %? stay with them and only ( ) %? switch to the other brand, as opposed to Special B where only ( )%? stay with them and ( )%? switch. (b) What are the projected market shares for the two brands? (Enter exact numbers as integers, fractions, or decimals.) Special B?1=? MDA?2=?
The Tiger Sports Shop1 has hired you as an analyst to understand its market position with respect to Clemson merchandise. It is particularly concerned about its major competitor, Mr. Knickerbocker, and which Clemson-related store has the ‘lead’ market share. Recent history has suggested that which Clemson-related store has the ‘lead market share’ can be modeled as a Markov Chain using three states: TSS (Tiger Sports Shop), MK (Mr. Knickerbocker), and Other Company (OC). Data on the lead market share is taken monthly and you have constructed the following one-step transition probability matrix from past data in the picture. a) The current state of the lead market share in October is that Tiger Sports Shop is in the lead (i.e., the Markov Chain in October is TSS). Tiger Sports Shop is considering launching a new brand in February only if it has the lead market share in January. Determine the probability that TSS will launch this new brand. Please show any equations or matrices…
Employment Employment Last Year This Year Percentage Industry Industry 80 Small Business 10 Self-Employed 10 Small Business Industry 10 Small Business 60 Self-Employed 30 Self-Employed Industry 10 Small Business 80 Self-Employed 10 Assume that state 1 is Industry, that state 2 is Small Business, and that state 3 is Self-Employed. Find the transition matrix for this Markov process. P =
(i) If volume is high this week, then next week it will be high with a probability of 0.8 and low with a probability of 0.2. (ii) If volume is low this week then it will be high next week with a probability of 0.2. Assume that state 1 is high volume and that state 2 is low volume. (1) Find the transition matrix for this Markov process. ... P = ... ... ... (2) If the volume this week is high, what is the probability that the volume will be high two weeks from now? (3) What is the probability that volume will be high for three consecutive weeks? ...
If she made the last free throw, then her probability of making the next one is 0.7. On the other hand, If she missed the last free throw, then her probability of making the next one is 0.2. Assume that state 1 is Makes the Free Throw and that state 2 is Misses the Free Throw. (1) Find the transition matrix for this Markov process. %3D
(i) If volume is high this week, then next week it will be high with a probability of 0.6 and low with a probability of 0.4. (ii) If volume is low this week then it will be high next week with a probability of 0.1. Assume that state 1 is high volume and that state 2 is low volume (1) Find the transition matrix for this Markov process. (2) If the volume this week is high, what is the probability that the volume will be high two weeks from now? (3) What is the probability that volume will be high for three consecutive weeks?
Anne and Barry take turns rolling a pair of dice, with Anne going first. Anne’s goal is to obtain a sum of 3, while Barry’s goal is to obtain a sum of 4. The game ends when either player reaches his goal,and the one reaching the goal is the winner. Define a Markov Chain to model the problem.
Three components are connected to form a system as shown in the accompanying diagram. Because the components in the 2-3 subsystem are connected in parallel, that subsystem will function if at least one of the two individual components functions. For the entire system to function, component 1 must function and so must the 2-3 subsystem. 2 The experiment consists of determining the condition of each component [S (success) for a functioning component and F (failure) for a nonfunctioning component]. (Enter your answers in set notation. Enter EMPTY or for the empty set.) (a) Which outcomes are contained in the event A that exactly two of the three components function? A = x (b) Which outcomes are contained in the event B that at least two of the components function? B = (c) Which outcomes are contained in the event C that the system functions? C = (d) List outcomes in C'. C' = List outcomes in A u C. AUC= List outcomes in An C. An C= List outcomes in Bu C. BUC= List outcomes in B n C.. BAC…
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.)
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A beauty salon employs three hairdressers. All customers get their hair washed in one area of the saloon before being taken to another area to get their hair cut. Customer arrival rate is considered deterministic (appointment only) and service time follows the exponential distribution. What is the Kendall notation for this system? O D/M/3 OM/G/3 O M/M/1 OM/M/3
Determine whether the statement below is true or false. Justify the answer. If (x) is a Markov chain, then X₁+1 must depend only on the transition matrix and xn- Choose the correct answer below. O A. The statement is false because x, depends on X₁+1 and the transition matrix. B. The statement is true because it is part of the definition of a Markov chain. C. The statement is false because X₁ +1 can also depend on X-1 D. The statement is false because X₁ + 1 can also depend on any previous entry in the chain.

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