Consider a bug starting at the origin of an in?nite lattice L and walking one unit north, south, east, or west at each discrete time t. The bug cannot stay still at any step. Let x1:t denote the sequence of coordinates (i.e., the path) of the bug up to time t, say {xi = (vi,w i):i = 1,…,t} with x0 = (0,0). Let the probability distribution for the bug’s path through time t be denoted ft(x1:t) = f1(x1)f2(x2|x1),…,f t(xt|x1:t-1). De?ne Dt(x1:t) to be the Manhattan distance of the bug from the origin at time t, namely Dt(x1:t) =| vt|+|wt|. Let Rt(v,w) denote the number of times the bug has visited the lattice point (v,w) up to and including time t. Thus Rt(xt) counts the number of visits to the current location. The bug’s path is random, but the probabilities associated with moving to the adjacentlocationsattimet arenotequal.Thebugpreferstostayclosetohome(i.e.,near the origin), but has an aversion to revisiting its previous locations. These preferences are expressed by the path distribution ft(x1:t) ? exp{-(Dt(xt)+Rt(xt)/2)}. a. Suppose we are interested in the marginal distributions of Dt(xt) and Mt(x1:t) = max(v,w)?L{Rt(v,w)}where the latter quantity is the greatest frequency with which any lattice point has been visited. Use sequential importance sampling to simulate from the marginal distributions of Dt and Mt at time t = 30. Let the proposal distribution or envelope gt(xt|x1:t-1) be uniform over the four lattice points surrounding xt-1. Estimate the mean and standard deviation of D30(x30) and M30(x1:30). b. Letgt(xt|x1:t-1)beproportionaltoft(x1:t)ifxt isadjacenttoxt-1 andzerootherwise. Repeat part (a) using this choice for gt and discuss any problems encountered. In particular, consider the situation when the bug occupies an attractive location but arrived there via an implausible path. c. A self-avoiding walk (SAW) is similar to the bug’s behavior above except that the bug will never revisit a site it has previously occupied. Simulation of SAWs has been important, for example, in the study of long-chain polymers [303, 394, 553]. Let ft(x1:t) be the uniform distribution on all SAWs of length t. Show that by using gt(xt|x1:t-1) = ft(xt|x1:t-1), the sequential update speci?ed by wt = wt-1ut isgiven by ut = ct-1 where ct-1 is the number of unvisited neighboring lattice points adjacent to xt-1 at time t -1. Estimate the mean and standard deviation of D30(x30) and M30(x1:30). Discuss the possibility that the bug becomes entrapped. d. Finally, try applying the simplistic method of generating SAWs by simulating paths disregarding the self-avoidance requirement and then eliminating any selfintersecting paths post hoc. Compare the ef?ciency of this method to the approach in part (c) and how it depends on the total number of steps taken (i.e., t = 30).

 

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11) One reason why economists often use models in their analysis is that

A) a model helps us to understand, explain, and predict economic phenomena in the real world.

B) a model accurately pictures every detail of the real world economy.

C) a model relates to individual thought processes rather than behavior.

D) it is relatively easy to perfectly specify a model.

12) An economic model should capture

A) the essential relationships that help to analyze the problem.

B) all possible variables that apply to the problem.

C) only social value related variables.

D) all of the above.

13) One problem with constructing a perfectly complete realistic economic model is that

A) it would be too simplistic to have any value.

B) it would be far too complicated to analyze.

C) politicians see little value in such a model.

D) None of the above is true.

14) Which of the following statements is true?

A) No economic model captures every detail that affects a problem.

B) Economic models always make accurate predictions about behaviors.

C) Economic models must fully reflect reality.

D) Economic models use economists' opinions with no use of data.

15) A map is an example of a model because a map

A) realistically describes an area.

B) is always as complex as space will permit.

C) is two-dimensional.

D) is a simplified representation of reality.

16) Holding all variables constant but one and assessing the impact of the one variable that has changed is an example of using

A) the ceteris paribus assumption.

B) an economic model based on unrealistic assumptions.

C) a flawed economic model.

D) an untestable proposition.

17) The term ceteris paribus means

A) the greatest good for all.

B) the study of scarcity and choice.

C) all other things remaining constant or equal.

D) value-free and testable.

18) In order to study how changing price affects consumer decisions, we must assume all other factors, such as income and the prices of other goods are constant.  This assumption is best know as

A) rationality.

B) ceteris paribus.

C) normative economics.

D) behavioral economics.

19) Which of the following is an example of an application of the ceteris paribus assumption?

A) An analysis of how price changes affect how much of a good people will purchase when all other factors are held constant

B) An analysis of how people purchase more goods when prices decline and income increases

C) After reading an article on the dangers of high-fat diets, an individual buys less red meat when prices increase

D) An analysis of how worker productivity increases when a firm invests in new machines and training programs

20) Ceteris paribus means

A) making all the necessary changes.

B) other things constant.

C) for certain parameters.

D) let the buyer beware.

 

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Create a site specification based on the information you developed in Week 1. Make sure to add mission statement; how to measure site success; description of intended audience; how to determine user satisfaction; and technological issues that might influence site development. Prepare a detailed page layout design in Visio including header area; link area; main content area; and footer area. This layout will be the main design/template for all of the pages in your site. In future weeks, you will be altering the main content areas as needed. Upon completion, name your single, MS Word document as lastname_CIS363A_projectWk2.

 

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What are the six steps in designing accounting based performance

What are the six steps in designing accounting-based performance measures?

What are the six steps in designing accounting based performance

 

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