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- A car servicing station has 2 bays where service can be offered simultaneously. Because of space limitation, only 4 cars are accepted for servicing. The arrival pattern is Poisson with 12 cars per day. The service time in both the bays is exponentially distributed with µ = 8 cars per day per bay. Find the average number of cars in the service station, the average number of cars waiting for service and the average time a car spends in the system.Normally when you look at something, your left and right eyes take in very similar images, and your brain blends them together, However, if totally different images are shown to each eye, the brain does something wild: it perceives one image for a brief time, then switches again and again. To model this process, we posit that there are two populations of neurons with average firing rates x1 and x2. These two populations battle for dominance, resulting in a model for neuronal competition: x'1 = -x1 + F(I - bx2) x'2 = -x2 + F(I - bx1) Here F(x) = 1/(1 + e-x) is a "gain function", I > 0 is the strength of the input stimulus, and b > 0 is the strength of the antagonism between neuron groups. a) Interpret the terms in this model in words. b) Sketch phase portaits for the following values of I and b: I = 1, b = 2; I = 1, b = 4; I = 1, b = 8. Discuss what you observe. What type of bifurcation do you see? c) Show that there is always a symmetric fixed point at x* = x*1 = x*2 for any…Normally when you look at something, your left and right eyes take in very similar images, and your brain blends them together, However, if totally different images are shown to each eye, the brain does something wild: it perceives one image for a brief time, then switches again and again. To model this process, we posit that there are two populations of neurons with average firing rates x1 and x2. These two populations battle for dominance, resulting in a model for neuronal competition: x'1 = -x1 + F(I - bx2) x'2 = -x2 + F(I - bx1) Here F(x) = 1/(1 + e-x) is a "gain function", I > 0 is the strength of the input stimulus, and b > 0 is the strength of the antagonism between neuron groups. a) Show that the Jacobian at this symmetric fixed point has delta = 1 - b2(x* - (x*)2)2 and Tau = -2. Argue that for large enough b the stability of the fixed points ches from a stable node to a saddle. b) Does this model exhibit the binocular rivalry switching behavior observed in experiments?
- Explain the term "Autoregressions"? Define The First-Order Autoregressive Model?Consider the following population model for household consumption: cons = a + b1 * inc+ b2 * educ+ b3 * hhsize + u where cons is consumption, inc is income, educ is the education level of household head, hhsize is the size of a household. Suppose a researcher estimates the model and gets the predicted value, cons_hat, and then runs a regression of cons_hat on educ, inc, and hhsize. Which of the following choice is correct and please explain why. A) be certain that R^2 = 1 B) be certain that R^2 = 0 C) be certain that R^2 is less than 1 but greater than 0. D) not be certainne- Brainfuse Whiteboard nfuse.com/jsp/user/userSessionFramesHTML5.jsp?event_id%36545060&user=21126002298071&#DesktopChatPlacej=90AE0C2DODD3CDD2C2B272B0E64 y 1 12 36 108 324 4. Is this LINEAR or EXPONENTIAL? Equation:
- An agricultural field trial compares the yield of two varieties of corn. The researchers divide in half each of 8 fields of land in different locations and plant each corn variety in one half of each plot. After harvest, the yields are compared in bushels per acre at each location. The 8 differences (Variety A - Variety B) give x¯=3.07 and s=5.11. Does this sample provide evidence that Variety A had a higher yield than Variety B? (a) State the null and alternative hypotheses: (Type "mu" for the symbol μμ , e.g. mu > 1 for the mean is greater than 1, mu < 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1)H0 : Ha : (b) Find the test statistic, t = 7,6If a model has inputs aligned so that x = the numberof years after 2000, what inputs would be used torepresent 2015 and 2022?An agricultural field trial compares the yield of two varieties of corn. The researchers divide in half each of 8 fields of land in different locations and plant each corn variety in one half of each plot. After harvest, the yields are compared in bushels per acre at each location. The 8 differences (Variety A - Variety B) give ī = 3.28 and s = 2.14. Does this sample provide evidence that Variety A had a higher yield than Variety B? (a) State the null and alternative hypotheses: (Type "mu" for the symbol u , e.g. mu >1 for the mean is greater than 1, mu <1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1) Ho : 0 Ha : 0 (b) Find the test statistic, t = (C) Answer the question: Does this sample provide evidence that Variety A had a higher yield than Variety B? (Use a 5% level of significance) (Type: Yes or No)
- A firm that operates a large, direct-to-consumer sales force would like to implement a system to monitor the progress of new agents. A key task for agents is to open new accounts; an account is a new customer to the business. To build such a system, the firm has been monitoring sales of new agents over the past 2 years. The response of interest is the profit to the firm (in dollars) of contracts sold by agents over their first year. Among the possible predictors of this performance is the number of new accounts developed by the agent during the first 3 months of work. Complete parts (a) through (f) below.A firm that operates a large, direct-to-consumer sales force would like to implement a system to monitor the progress of new agents. A key task for agents is to open new accounts; an account is a new customer to the business. To build such a system, the firm has been monitoring sales of new agents over the past 2 years. The response of interest is the profit to the firm (in dollars) of contracts sold by agents over their first year. Among the possible predictors of this performance is the number of new accounts developed by the agent during the first 3 months of work.Evolution determines the change in inherited traits over time to ensure survival. There are three variants identified as Variant 1 with high reproductive rate, eats fruits and seeds; Variant 2, thick fur, produces toxins; and Variant 3 with thick fur, fast and resistant to disease. These variants are found in a cool, wet, and soil environment. In time 0 years with cool and wet environment, the population is 50,000 with 10,000 Variant 1. 15,000 Variant 2, and 25,000 of Variant 3. Two thousand years past, the environment remained the same with constant average temperature and rainfall. A disease spread throughout the population. However the population increased to 72,000. Calculate the population percentage of each variant in 0 years.
