Alex only eats dinner at Henry's Tavern or Felicity's. However, he refuses to eat at Felicity's two days in a row. If he eats at Henry's Tavern, there is an equal chance that he'll eat at Henry's Tavern or that he'll eat at Felicity's the next day. Model this scenario using a Markov chain with two states, Henry's Tavern and Felicity's. 1. Write the transition matrix for this Markov chain.
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- Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.Consider there are only two computer companies in a country. The companies are named “Dude” and “Imac”. Each year, company Dude keeps 1/5th of its customers, while the rest switch to Imac. Each year, Imac keeps 1/3rd of its customers, while the rest switch to Dude. If in 2002, Dude has 1/6th of the market and Imac has 5/6th of the market, what is the distribution of the market share between the two companies in 2003. (Hint: you can cast this as a matrix multiplication problem)Two players, A and B, are playing an asymmetrical game. There are n points on the game board. Each turn player A targets a pair of points and player B says whether those two points are connected or unconnected. A can target each pair only once and the game ends when all pairs have been targeted. Player B wins iff a point is connected with all other points on the very last turn, while player A wins if any point is connected with all other points on any turn but the very last one OR if no point is connected to all other points after the last turn. For what values of n does either player have a winning strategy?
- The following economic model predicts whether a voter will vote for an incumbent school board member INCUMBENT= B1 + B2 MALE+ B3 PARTY+ B4 MARRIED+ Bs KIDS where INCUMBENT= 1 if the voter votes for them, 0 otherwise, MALE=1 if the voter is a male, PARTY = 1 if the voter is registered with the same political party as the incumbent, MARRIED= 1 for married voters, 0 otherwise, and KIDS is the number of school age kids living with the voter. What is the probability that a married woman without kids who is not registered with a political party will vote for the incumbent? b. What is the probability that a married male with 2 kids and registered with the same party as the incumbent will vote for the incumbentA researcher is interested in understanding how the flexibility of vacation policies at a company influence employee satisfaction with their job. Company 1, Vance Refrigeration, has a 2 week vacation policy in which employees can take those 2 weeks at any time during the year. Company 2, Dunder Mifflin Paper Company, has a 2 week vacation policy in which employees can only take vacation days during specific pre-approved times of year. How could the confound be fixed for Scenario A? Be sure to tell me what technique you are using (constancy, repeated measures, randomization, elimination, or balancing), as well as how you would apply that technique to this specific scenario, and how that would fix this confound.1. Grocery store A and grocery store B are located close to where you live. Store A does not replace inventory until the next day. Store B replaces inventory in real time (i.e. as soon as an item is purchased, it is restocked). Every day, both stores have the following chocolate bars available for purchase; 50 Butterfingers, 65 Hershey Almond bars, 30 Nestle Crunch bars, and 80 Luna bars. (a) On any given day, if you purchase 6 chocolate bars from store A, what is the probability that 3 are Luna bars, 2 are Nestle Crunch bars and 1 is a Hershey Almond bar? (b) SAME question as (a) above, except this time you buy the chocolate bars from store B.
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- A biologist wonders if the life span of bats will be affected by two new food sources from invasive species moving into an area. To conduct the experiment, the biologist needs three treatment groups: a group where the diet will not include invasive species (control), a group where the diet will include one invasive species (treatment group 1), and another group where the diet will include the other invasive species (treatment group 2). The biologist chooses the first cloud-free night and catches the first 18 bats that fly out of a cave, placing them into three equal groups of six bats. To decide the treatment for each group, the biologist places three slips of paper labeled control, treatment group 1, and treatment group 2 in a hat and randomly selects 2 slips of paper. The first piece of paper gives the treatment for the first group, the second piece of paper gives the treatment for the second group, and the remaining treatment is given to the third group. Which component is…A biologist wonders if the life span of bats will be affected by two new food sources from invasive species moving into an area. To conduct the experiment, the biologist needs three treatment groups: a group where the diet will not include invasive species (control), a group where the diet will include,one invasive species (treatment group 1), and another group where the diet will include the other invasive species (treatment group 2). The biologist chooses the first cloud-free night and catches the first 18 bats that fly out of a cave, placing them into three equal groups of six bats. To decide the treatment for each group, the biologist places three slips of paper labeled control, treatment group 1, and treatment group 2 in a hat and randomly selects 2 slips of paper. The first piece of paper gives the treatment for the first group, the second piece of paper gives the treatment for the second group, and the remaining treatment is given to the third group. Which component is missing…2. The Bernoulli family is comprised of two parents named A and B, and three children named C, D, and E. Any major decision must have the approval of at least one parent and two children. With an example, show that this system is NOT Swap-Robust.