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Question: Languages. The symbols of a language can be considered to be generated by a Markov process. As a Simple example consider a language consisting of the symbols A, B, and S (space). The space divides the symbol sequence into words. In this language two B's or two S's never occur together. Three A's never occur together. A word never starts with AB or ends with BA. Subject to these restrictions, at any point, the next symbol is equally likely to any of the allowable possibilities.
- Formulate a Markov chain for this language. What are the equilibrium symbol probabilities? (Hint: Let some states represent pairs of symbols.)
US Airways conducted a number of studies that indicated a substantial savings could be obtained by encouraging Dividend Miles frequent flyer customers.
What is the optimal production plan, assuming that the optimality criterion is the minimum expected cost? Assume that λ1= 3, λ2 = 5, λ3 = 2, λ4 = 4 units.
You have been recently employed as the director of operations of a hotel. The hotel is in a relatively large city with many other comparable hotels in its vicinity. As part of your job, your responsibilities include:
Amy and Vince want to save $8,000 so that they can take a trip to Europe in four years. How much must they save each month to have the money they need if they can get 6%, compounded monthly, on their savings?
Simple differential equation modelling the smoke layer depth (y) in a large atrium provided with dynamic smoke extraction system.
What is the expected value of operations when constant growth begins?
Calculate the cost of each individual sale separately using LIFO procedures. The firm uses the perpetual inventory system, and there are 52 units of the item on hand at the end of the year. What is the total cost of the ending inventory according ..
Using Taylor series expansion derives the error term for the following formulas: Use method of undetermined coefficients to derive second order scheme for ∂u/∂x using three points in the following way
Choose any of the Perspective boxes in this chapter or the opening case. Then, identify and describe at least seven metrics that could be used to measure the success of the IT systems in your chosen example. For each metric, categorize it as eit..
The perpetual American call option is a call option that can be exercised at any time in the future and never expires. What will its value be in a positive-interest-rate world?
Variation of Parameters. The classic derivation of the general solution formula for a homogeneous system of differential equations is based on a method.
Researchers routinely choose an alpha level of 0.05 for testing their hypotheses. What are some experiments for which you might want a lower alpha level (e.g., 0.01)? What are some situations in which you might accept a higher level (e.g., 0.1)?
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