Answered: 0|0|0|0 - Consider the time series X₁… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 18T

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Consider the time series X₁ and Y₁ = (I – B)² (I – B³)Xt. What transformations were
performed on Xt to obtain Yt?
seasonal difference of order 2
simple difference of order 5
seasonal difference of order 1
seasonal difference of order 5
simple difference of order 2

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Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
Suppose Ct is the concentration of a drug in the bloodstream at time t, A is the concentration of the drug that is administered at each time step, and k is the fraction of the drug metabolized in a time step. (a) What is the recursion that models the dynamics of drug concentration? Ct+1 = (b) If the initial concentration is Co 200 150 100 50 200 150 100 50 Ct Ct 2 2 4 = 110 µg/mL and A = 80 µg/mL and k = 6 8 …... 6 CO 8 10 t 10 120 100 80 60 40 20 150 Ct 100 1 2' 50 plot some points on the graph of Ct. 2 2 4 4 8 6 ….... 10 8 t 10
Figure 7(a) shows the correlogram of a stationary time series; Figure 7(b) shows the partial correlogram. Autocorrelation 1.0 (a) 0.5- 0.0 -0.5- -1.0- (a) Figure 7(a) & (b) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Lag Partial autocorrelation 1.0 0.5- 0.0 -0.5- -1.0- 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Lag (b) Use the correlogram and partial correlogram to identify two plausible ARMA models for this time series. Explain carefully the reasons for your choices. (b) Use the principle of parsimony to identify which, if either, candidate model is 'better' from the pair you selected in part (a).
Suppose that the stationary time series {x, : t = T} satisfies the equation: x₁ =B₁ X-1 + B₂ x₁-12 - B1 B₂ x₁-13 + U₁ Determine the autocorrelation function of {x, :t € T}. Plot the autocorrelation function with ₂ = 0.6, B₁ = -0.1.
3. For r = 3.2 and r = 3.5, calculate the first 100 sequence values. Generate a cobweb diagram for each iterative process. (Several free applets are available online that generate cobweb diagrams for the logistic map.) What is the long-term behavior in each of these cases?
Assume that the population size of honey bees in billions at year t is hy, and the population size of wild bees in billions at year t is uy. They follow the following recursive relationship: ht +1 = 2he - 4, ut +1 = 0.5ut + 1 EQUATIONS ARE IN IMAGE Currently, there are 5 billion honey bees (ho = 5) and 10 billion wild bees (wo = 10). Find an explicit formula for the population of honey bees. Find an explicit formula for the population of wild bees. What will be the population of wild bees in a long run (as t → ∞). If each honey bee can pollinate 1000 plants annually and wild bees pollinate 2000 plantseach year, how many plants will be pollinated in billions in the current year (f = 0), and after 2years (t = 2)? Compare the results and assess whether the pollination rate is likely to decrease inthe near future or not.
Exer. 81-82: When computations are carried out on a cal- culator, the quadratic formula will not always give accurate results if b' is large in comparison to ac, because one of the roots will be close to zero and difficult to approximate. (a) Use the quadratic formula to approximate the roots of the given equation. (b) To obtain a better approximation for the root near zero, rationalize the numerator to change ーb± VF - 4ac 20 to r = 2a ーb VF - 4ac and use the second formula. 81 x? + 4,500,000x – 0.96 = 0 82 x? - 73,000,000x + 2.01 = 0
Number 4
06). A machine its cycle of operations every time as firm pulley completes a revolution. The displacement f(x) of a point on a certain portion of the machine is given in the table given below for six positions of the pulley, x being the angle turned through by the pulley. Find the Fourier series to represent f(x) for all values of x (CLO - 2) x in degrees S(x) 60 120 180 240 300 360 7.129 4.495 1.215 0.141 L.199 5.985
Q.1*** Write the Fourier series of the following function on the given intervals. i. f (x) = 1 – |x|, - 2 < x < 2 -4, for – n

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