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- ARCH(1) model o? = w+ ae?_1. Define Y; = e? and u: = e? – o?. %3D Show that Y, can be written as a specific autoregressive process with innovation u.9. Evaluate x³+1 x+2 a. b. x3 x3 C. dx x³ + x² + 4x + 7 ln(x + 2) + C x² d. x3 + 4x ln(x + 2) + C 2 - ·x² + 4x - 7 ln(x + 2) + C + x² + 4x - In(x + 2) + C 33.) Johns Hopkins reports two numbers daily for all the US states: P(t): the total number of cases confirmed on day t or before N(t): number of new cases reported on day t a.) What is P(t+1)-P(t) in terms of N? b.) Compare (P(t+1))-(P(t))/1 with (P(t-Δ))-(P(t))/Δt What is the value of Δt and explain why P ≈ N in words.
- A model is built to explain the evolution of spending on tourism and recreation in a certain group of families (Y in USD/person/year). As potential explanatory variables are considered: X1 average annual income per person in the family (in USD), X2 – number of people in the family, X3 – nature of employment of the head of household If X3=1, when the head of the family is self-employed, X3=0, when the head of the family is an employee Based on the collected data, linear correlation coefficients between variables were calculated and obtained 0,84 R, = -0,47 [1 -0,55 0, 62 R= 1 -0,42 0,75 1 Using Hellwig's method, select the optimal combination of explanatory variables for the tourism and recreation expenditure model.Suppose the entire cola industry produces only two colas. Given that a person last purchased cola 1, there a 70% chance that her next purchase will be cola 1. Given that a person last purchased cola 2, there is an 75% chance that her next purchase will be cola 2. Suppose that each customer makes one purchase of cola during any week (52 weeks=1 year). Suppose there are 150 million customers. One selling unit of cola costs the company $0.5 to produce and is sold for $2. For $200 million per year, Britney Spears (by an advertising song) guarantees to decrease from 30% to 15% the fraction of cola 1 customers who switch to cola 2 after a purchase. Should the company that makes cola 1 hire Britney Spears?(a) Write a function of the form P (t) = Poet to model each population P (t) (in millions) / years after January 1, 2000. Round the value of k to five kt decimal places. Country Congo Turkey Population in 2000 (millions) 50 67.4 Population in 2010 (millions) 66 73.7 P (t) = Pekt P(1) = I 0 P (t) = e X S
- Let W = {A E M33 : a11 = a12 = 0 and az21 = a22}. Then %3D %3D dim(W) = (A) 4 (B) 8 (C) 7 (D) 5 (E) 6A building contains 1000 lightbulbs. Each bulb lasts at most five months. The company maintaining the building is trying to decide whether it is worthwhile to practice a “group replacement” policy. Under a group replacement policy, all bulbs are replaced every T months (where T is to be determined). Also, bulbs are replaced when they burn out. Assume that it costs $0.05 to replace each bulb during a group replacement and $0.20 to replace each burned-out bulb if it is replaced individually. How would you use simulation to determine whether a group replacement policy is worthwhile?Consider the discrete time model for population growth: Na+1 = Ne"(1-N,) with r > 0. (a) Find all steady states. (b) Discuss the stability of each steady state.
- Construct a model for the number of cats, y, after x months that make use of the following assumptions: 1. It begins with two cats – one female and one male, both unneutered. 2. Each litter is composed of 4 kittens – 3 males and 1 female. 3. It takes four months before a new generation of cats is born. 4. No cat dies (all are healthy) and no new cats are introduced.ASIACELL LTE 5:51 PM 36% A cis.turath.edu.iq 2 of 6 Determine the Domain •B. and the Ran ge of the Fallowing fun etions 1. Fux = 6x+ 2 2 Faw = x²- 2x + 6 3. Fer)= -| + 2x - x? 4. F&) = X - 3X x²- 3x² - 5 x + 15 5. hcx)z 2K + 6 X -4 X - 12 NB. Solving s Graphing the functions are required A. Find fo llow ing Functions the inuerse of theFreddy is the owner of Freddy’s fast fuel for Small Aircraft specializing in “Providing flight fit fantastic fuel” for small general aviation aircraft such as a Cessna 172. Freddy is experimenting with a fueling process involving new equipment and is trying to determine if the current process takes more time than the new process with the new equipment he is experimenting with. If the current process takes more time than the new process, Freddy will purchase some new, rather expensive fueling equipment to use across several small general aviation airports his company services. Freddy is comparing sample mean times to evaluate his hypothesis about the population (total number of aircraft fuel fill-ups). Over the period of a week, he took a random sample of fuel fill-up times using both the old and new processes. Using the information Freddy provided, you ran a t-test for independent samples. These are the results (α = .05). t-Test: Two-Sample Assuming Unequal Variance Current…
