Suppose the rate of inflation in year t, It, is to be modelled by the AR(1) It - 0.0182 = 0.42(It−1 − 0.0182) + 0.042Zt - where Z₁~N[0,1] The current (period 0) annual rate of inflation is 5.3% (1 = 0.053). b) Find the distribution of I₁. Provide the necessary calculation.
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![Suppose the rate of inflation in year t, It, is to be modelled by the AR(1)
It = 0.0182 = 0.42(It-1 – 0.0182) + 0.042Zt
where Z~N[0,1]
The current (period 0) annual rate of inflation is 5.3% (1 = 0.053).
b) Find the distribution of I₁. Provide the necessary calculation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4add683a-b7f7-4eb2-9ccd-ba51ac12c93a%2Fe445a721-8fe3-4b71-9cb0-a9ffa6c5c101%2Fplca64m_processed.png&w=3840&q=75)
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- Table 2 shows a recent graduate’s credit card balance each month after graduation. a. Use exponential regression to fit a model to these data. b. If spending continues at this rate, what will the graduate’s credit card debt be one year after graduating?Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.Recent data suggests that, as of 2013, the rate of growth predicted by Moore’s Law no longer holds. Growth has slowed to a doubling time of approximately three years. Find the new function that takes that longer doubling time into account.
- The number of cases within 3 days due to coronavirus is as follows: 21 May 2020: 961 New Case 22 May 2020: 952 New Case 23 May 2020: 1186 New Case 1a) Calculate the growth rate according to this information and express this variable as X = Aert. 2a) Using the answer 1a, Make a prediction for the previous and next day of the end date you use in your calculations.The following table shows total military and arms trade expenditure for a certain country in 2000, 2006, and 2012. Year t (year since 2000) 12 Military Expenditure C(t) ($ billion) 390 590 680 (a) Compute the average rate of change of C(t) over the period 2006-2012 (that is, [6, 12]). Be sure to state the units of measurement. HINT [See Example 1.] ---Select-- Interpret the average rate of change. This country's military expenditure increased at an average rate of about v between 2006 and 2012. --Select--- (b) Compute the average rate of change of C(t) over the period [0, 12]. Be sure to state the units of measurement. HINT [See Example 1.] (Round your answer to two decimal places.) -Select--- Interpret the average rate of change. (Round your answer to two decimal places.) This country's military expenditure increased at an average rate of about -Select-- v between 2000 and 2012. Need Help? Read It Master It(d) At any time, find the mean age of insects in the population. (e) Sketch g(x), the p.d.f. of the age distribution of insects in the population. (f) No calculations are required for this part of the question.Now suppose that a population with the life table function Q(x) thatyou obtained in part (b) is stable but not stationary. Describe brieflyhow the age distribution of the population would differ from that of astationary population with the same life table function if the populationis (i) growing, (ii) declining. Draw rough sketches to show what thep.d.f. of the age distribution might look like in each case.
- The following table shows total military and arms trade expenditure for a certain country in 2000, 2006, and 2012. Year t (year since 2000) 6 12 Military Expenditure C(t) ($ billion) 330 530 620 (a) Compute the average rate of change of C(t) over the period 2006-2012 (that is, [6, 12]). Be sure to state the units of measurement. HINT [See Example 1.] ---Select- Interpret the average rate of change. This country's military expenditure increased at an average rate of about ---Select--- v between 2006 and 2012. (b) Compute the average rate of change of C(t) over the period [0, 12]. Be sure to state the units of measurement. HINT [See Example 1.] (Round your answer to two decimal places.) ---Select-- Interpret the average rate of change. (Round your answer to two decimal places.) This country's military expenditure increased at an average rate of about ---Select-- v between 2000 and 2012.A model for lifetimes, with a bathtub-shaped hazard rate, is the ex- ponential power distribution with survivai function S(x) = exp{1 exp((A.x)"]}. – (a) If a = 0.5, show that the hazard rate has a bathtub shape and find the time at which the hazard rate changes from decreasing to increasing. (b) If a = 2, show that the hazard rate of x is monotone increasing.5.1 (1) The graph shows the population of bacteria in a culture. a) Determines the average rate of variation of the crop between the 3rd and 4th hour. B) What does this rate of change mean?
- The rate of growth of a population of a city is given by: P' = 2000t1.04 where P is the population and t is the number of years past 2015. If the population in the year 2015 is 50,000, what is the predicted population in the year 2025? O 107,498 5.45 Billion O 746,943 O 157,498On the basis of the quarterly sales (in lakhs Rs.) of a certain commodity for the year (1994-98), the following calculations were made :The following table gives the profits of a concern for 5 years ending 1983 : Year : 1994 1995 1996 1997 1998 Profits (in '000 Rs.): 1.6 4.5 13.8 40.2 12.5 Fit an equation of the type Yc abx
