ne bets $1.0.45, he wins the game and with probability 1 - p = 0.55, he loses thegame. His goal is to increase his capital to $3, and as soon as he does, the game is over. The game is alsoover if his capital is reduced to zero. Construct an absorbing Markov chain and answer the followingquestions.• What is the expected duration of the game?• What is the probability that he goes broke?

* SOLUTION :- From the given information the calculation is provided as below as

Answered: ne bets $1. 0.45, he wins the game and…

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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Assume that a website www.funwithmath1600.ag has three pages: • Page A: King Algebra • Page B: Learn1600andWin Page C: Linear AlgbraIsEverywhere Each page has some links to the other pages of this website and no pages links to any page outside this website. • Page A has three links to page B and only one link to page C. • Page B has three links to page A and two links to page C. • Page C has one link to page A and two links to page B. A student decides to explore this website starting from page A. Since reading content is always a boring task (is it?!) they decide to choose one of the links in page A with equal probability and click on the link to see the next page. As a result, on the next step, they will end up on page B with probability 3/4 and on the page C with probability 1/4. This process is then continued by the student with the same rule: Go the next page by clicking, with equal probability, on one of the existing links that are on the present page. (Use only fractions in your…
2. This year Karen has decided to diversify her business by growing broc- coli as well as lettuce. Karen plants lettuce with a probability of or broccoli with a probability of . By the time these plants are ready to harvest the price of lettuce increases with a probability of and decreases with a probability of 3. The price of broccoli increases with a probability of , decreases with a probability of or stays the same with a probability of . (a) Draw a probability tree for this scenario. (b) Use the probability tree to determine the probability that Karen plants broccoli and that the price of broccoli increases by the time it is ready to harvest. (c) Use the probability tree to determine the probability that the price of whatever Karen plants increases by the time it is ready to harvest. (d) Calculate Pr(Price of lettuce does not change | Karen plants lettuce). (e) Calculate Pr(Price of broccoli does not changen Karen plants broccoli).
Mohammed has bought a television from Samsung at a cost of 400 R.O. He has an option of buying an extended service warranty offering 2 years of coverage for 35 R.O. After discussing with his friends and reading reports, Mohammed believes the probabilities of following maintenance expenses could be incurred during the next 2 years. EXpense(R.O) 0 15 30 45 60 75 Probability 22.75a 16.25a 65a 7.8a 5.2a 3.25a a.find tha value of a. b.find the expected value of the anticipated maintenance cost. c.find E(65x-8) d.find V(65x+7)
5
An airline offers "advance-purchase" fares to customers who buy their tickets at least four weeks before the flight. The airline has noticed that 80% of its customers who buy tickets don't take advantage of advance-purchase fares and the remaining 20% do. The no-show rate for those who don't have advance-purchase fares is 25%, while for those who do have them, it is only 15%. (a) Calculate the probabilities labeled on the tree diagram below. (Give answers correct to three decimal places.) A tree diagram with 6 branches is shown. The tree diagram begins at a point and an upper and lower branch extend from this point to the right. From each of these two branches two more upper and lower branches extend to the right. The branches extending from the first point from top to bottom are labeled a and b and end at points labeled "no advance purchase" and "advance purchase" respectively. The branches extending from "no advance purchase" and "advance purchase" from top to bottom are labeled…
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An investor has a certain amount of money available to invest now. Three alternative investments are available. The estimated profits, in Kwacha, of each investment under each economic condition are indicated in the following payoff table: Event Investment selection A B C Economy declines 500 -2000 -7000 No charge 1000 2000 -1000 Economy Expand 2000 5000 20,000 Based on his own past experience, the investor assigns the following probabilities to each economic condition: P (Economy declines) = 30 P (No Change) = 0.50 P (Economy expands) = 0.20 Determine the optimal action based on the maximax criterion Determine the optimal action based on the maximin criterion iii. Compute the expected monetary value (EMV) for each investment
Diane has decided to play the following game of chance. She places a $1 bet on each repeated play of the game in which the probability of her winning $1 is .4. She has further decided to continue playing the game until she has either accumulated a total of $3 or has lost all her money. What is the probability that Diane will eventually leave the game a winner if she started with a capital of $1? Of $2? capital of $1 capital of $2
Given the following Markov Chain diagram. 0.15 On Duty Off 0.85 0.2 Duty 0.8 Given that you were on duty the first day (i.e., P(Day 1=On Duty) = 1 and P(Day %3D 1= Off Duty) = 0), answer the following questions. • What is the probability that you need to report towork on the 2mnd day (i.e., P(Day 2 = On Duty))? Answer: (Please write your answer with 2 decimal points) • What is the probability that you take a leave on the 2nd day (i.e., P(Day 2 = Off Duty))? Answer: (Please write your answer with 2 decimal points) • What is the probability that you go to work on the third day (i.e., P(Day 3=On Duty))? Answer: |(Please write your answer with 4 decimal points) • What is the probability that the third day was a Day Off (i.e., P(Day 3=Day Off)? Answer: (Please write your answer with 4 decimal points)

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