2.12 Two urns contain k balls each. Initially, the balls in the left urn are all red and the balls in the right urn are all blue. At each step, pick a ball at random from each urn and exchange them. Let X, be the number of blue balls in the left urn. (Note that necessarily Xo = 0 and X, = 1.) Argue that the process is a Markov chain. Find the transition matrix. This model is called the Bernoulli-Laplace model of diffusion and was introduced by Daniel Bernoulli in 1769 as a model for the flow of two incompressible liquids between two containers. %3D
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- Two oil companies are deciding how much oil to extract from their properties, which lie above the same underground reservoir. The faster that oil is extracted, the less total oil is extracted. Letting x denote the extraction rate for company X and y denote the extraction rate for company Y, we assume that the total amount of oil extracted is 1/(x + y) million gallons of oil. Of the total amount that is extracted, the share going to company X is x/(x + y), and the share to company Y is y/(x + y); that is, a company’s share depends on how fast it extracts compared with the other company. The price of oil is $100 per gallon. Each company chooses its extraction rate from the interval [1,10] in order to maximize the monetary value of the oil that it extracts. Find the Nash equilibrium extraction rates. (Note: You can assume that the payoff function is hill shaped.)State the Gauss-Markov Theorem.What are the three Gauss–Markov conditions? Explain.
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- Let say you have 3 products: cake, candy, and bread. The revenue per cake is $8. The revenue per candy is $4. The revenue per bread is $5. Define the number of cake, candy, and bread you are about to produce per day as x, y, and z respectively. The manager wants that the number of candy is at least equal to the total number of cake and bread. What is the correct linear constraint to show this? Group of answer choices z – x – y ≥ 0 x – 2y – z ≥ 0 y – x – z ≥ 0 x – y – z ≥ 0The time path of resources is described by X(t) = X(0)e*". If you graphed In X(t) on the y-axis, and had time (t) on the x-axis, then what would be the intercept of the line you drew? In X(0) There isn't enough information to tell gxDetermine the Nash equilibria