Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful! 3. An office worker owns 3 umbrellas which she uses to go from home to work and viceversa. If it is raining in the morning she takes an umbrella (if she has one) on hertrip to work and if it is raining at night she takes an umbrella (if she has one) onher trip home. If it is not raining, she doesn't take an umbrella. At the beginningof each trip it is raining with probability p = 1 − q, independently of previous trips.Let X represent the number of umbrellas available at the beginning of the n-thtrip and assume that 0 < p < 1.(a) Explain why {X}n≥1 is a Markov Chain with state space Shaving the transition probability matrix P:0(144)001-p PP =01-p- PР0 0P 0={0, 1, 2, 3}(b) Classify the states of the Markov chain in (a) under additional condition 0 ≤p≤1.(c) Explain or calculate directly why P(X3 = 0 | X₁ = 0) = 1 − p.(d) If no umbrellas are available at the beginning of the first trip, calculate theaverage number of trips until there are again no umbrellas available.(e) Explain why the limits of P(Xncalculate them.=i) as n∞ exists, for i = 0, 1, 2, 3, and(f) After a large number of trips, how many umbrellas are available on average atthe beginning of a trip?(g) In a large number of trips, about what proportion of journeys does she getwet?

Let Xn represent the number of umbrellas available at the beginning of the nth trip and assume that…

Answered: 3. An office worker owns 3 umbrellas…

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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Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer. Very very grateful!