43.10. Permanent disability is modeled as a Markov chain with three states: healthy (state 0), disabled(state 1), and dead (state 2). You are given the following transition forces:0.05 5(1) =0.10 r>5(i) 4, =0.02(iii) p,-0.02Calculate the probability that a healthy person age x will be dead at age x +10.

The given model is a Markov chain model therefore, the probability of future state depends only on…

Answered: 13.10. Permanent disability is modeled…

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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4. A Markov chain has transition matrix 6 1 3 4 Given the initial probabilities ø1 = 02 = ¢3 = , find Pr (X1 X2). %3D %3D 1/4
A Markov Chain has the transition matrix P 3D 0. 1 and currently has state vector % %% . What is the probability it will be in state 1 after two more stages (observations) of the process? 6. (A) % 3/4 (B) 0 1/12 (D) ½4 (E) 2 /12 1/4 (G) 1 (H) 23/24 O A O B OD O E OF OG H.
5. consider the example below, where the states are Condition State and the transition matrix is 0 1 23 2 Πο Good as new Operable-minimum deterioration Operable-major deterioration Inoperable and replaced by a good-as-new machine we found that the steady-state probabilities are 2 13' T1= = P = 78314 00 1 0 7 13' HARTNO LELBLINO 1 16 1 1 1 1 16 8 8 0 2 2 = π2 2 13' I3 = 2 13 (a) Find the expected recurrence time for state 0 (i.e., the expected length of time a machine can be used before it must be replaced) by solving a linear system for Moo, M10, 20, and μ30. (b) Find the expected recurrence time for state O directly by the formula Moo 1 πο =
3. suppose that the manufacturer keeps a spare machine that only is used when the primary machine is being repaired. During a repair day, the spare machine has a probability of 0.1 of breaking down, in which case it is repaired the next day. Denote the state of the system by (x, y), where x and y, respectively, take on the values 1 or 0 depending upon whether the primary machine (x) and the spare machine (y) are operational (value of 1) or not operational (value of 0) at the end of the day. [Hint: Note that (0, 0) is not a possible state.] (a) Construct the (one-step) transition matrix for this Markov chain. (b) Find the expected recurrence time for the state (1, 0).
(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?
Consider a set of three assets, one risk-free and two risky. The covariance matrix [0.36 0.07] for the risky assets is given by = 0.07 The risk-free rate is 0.03 0.07 0.29 and risk aversion is A = 4. Calculate the optimal portfolio for this individual.
Classify the statement as an example of classical probability, emipirical probability, or subjective probability. In one state lottery, a person selects a 4-digit number. The probability of winning this state's lottery is 1/ 10,000
Question 4(a) Assume that the probability of rain tomorrow is 0.5 if it is raining today, and assume that the probability of its being clear (no rain) tomorrow is 0.9 if it is clear today. Also assume that these probabilities do not change if information is also provided about the weather before today.(i) Explain why the stated assumptions imply that the Markovian property holds for the evolution of the weather. (ii) Formulate the evolution of the weather as a Markov chain by defining its states and giving its (one-step) transition matrixb) i. consider the M/M/1 queue with arrival rate λ and service rate µ and explain how it can be modelled as a birth death model. ii. For the M/M/1 queue derive the form of , the equilibrium distribution of the number of customers present, and give any conditions needed to ensure the existence of the equilibrium distribution. Derive the mean value of the equilibrium distribution d) If an M/D/1 queue has utilization of 80% do you expect its mean queue…
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

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