Please answer ASAP Amazon has 100 million prime members. The annual prime membership feeis $100. Amazon is thinking about raising the prime membership fee to $150. By such a price increase30 million prime members will cancel their membership. However, those who remain a member aremore likely to buy from Amazon. The marketing department uses a Markov chain to model customerpurchase behavior. In each day a customer may buy from Amazon or other retail stores. When themembership price is $100, If a member customer buys from Amazon today, with probability 0.6 will buyfrom Amazon tomorrow; if a member customer buys from other retail stores today, with probability 0.5will buy from Amazon tomorrow. When the membership price is $150, If a member customer buys fromAmazon today, with probability 0.7 will buy from Amazon tomorrow; if a member customer buys fromother retail stores today, with probability 0.6 will buy from Amazon tomorrow. For simplicity assumethat a customer purchases once a day and the net value of each purchase to Amazon is $200. ShouldAmazon increase the prime membership fee? Why?

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Answered: Amazon has 100 million prime members.…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.5: Markov Chain

Problem 47E: Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.

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Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.
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…
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 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 0.04 0.96 (a) Which brand appears to have the most loyal customers? Explain. _____ has the most loyal customers because _____ % stay with them and only _____ % switch to the other brand, as opposed to _____ 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= _____
Mr. X owes a lot of money to the mafia. If he misses three weekly payments in a row, the mafia boss will lose her patience and Mr. X will be in big trouble (after which he will have larger problems than weekly payments). Let’s say that the probability that Mr.X misses a payment is 5%. Further, at any time, there is a probability of 2% that Mr. X manages to pull off a get-rich-quick scheme and pays off his debt. Model the system as a Markov chain so that you can then evaluate the probability to pay-offthe debt for Mr. X. Write down the transition matrix, identify matrices Q and R. Calculate the matrix N and find the probability that the debt is repaid. Find the expected time until payments are a non-issue one way or the other
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.
Central topic markov chains: Young Filibonio (who likes steak), Petronilo (who likes chicken) and Juventino (who likes ham) are frequently invited to eat at their friend Susiflor's house.frequently invited to eat at the home of their friend Susiflor, who only prepares these three dishes.They have decided to bet, before going to each meal, on which dish they will be served.The assumption is that if their hostess serves steak on one occasion, she will not serve it next time; she then flips a coin and serves chicken if it lands on the table.a coin and serves chicken if it lands eagle or ham if it lands sun.If on a certain occasion she serves chicken, for the next time she flips two dice, and will serve chicken if they both land on the same number; if on the first flip, she will serve chicken if they both land on the same number.number; if on the first roll of the dice different numbers fall, he throws them again, and he will serve steak if they fall on the samesame mark or ham…
The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities:
Topic: MARKOV CHAINS In a sample of 400 Internet subscribers taken in late 2000, 80% were connected by telephone, and the rest via cable modem.the rest via cable modem. At the end of 2001, the number of subscribers who switched from telephone to cable modem connection was 110; and the number of subscribers who switched from telephone to cable modem connection was 110.modem connection was 110; and the number of subscribers switching from cable modem to telephone connection was 24. A) Write the transition matrix of the problem.

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