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- Use sigma notation to write the Taylor series about x = 9 for the function. 1 x + 5 Σ k10:49 O O o d• V 4Í 91% Activity 4 All changes saved 1. Find the next two numbers of the following series: а) 31, 28, 31, 30, 31 b) 1, 2, 4, 7, 11 с) 3, 5, 9, 15, 236.4 Find the relationship between the A(k), B(k), and X(k), where X(k) are the expo- nential expansion coefficients and A(k) and B(k) are the trigonometric expansion coefficients for the discrete Fourier series of a real periodic sequence.
- The Maclaurin series Select one: x3x+2 Σ(-7)*- a. x²e-7x² O b. -7cos(x³)+2 O c. -7e³x+2 O d. x'sin(-7x³) represents which expression below?For each of the time series models below undertake the following steps: • Write each time series in characteristic polynomial form using backshift operator (MA or AR or ARMA polynomials as required) • Factorise the relevant polynomials and find the roots of the polynomials. • You are given the following additional information regarding the relationship between stationarity and the characteristic polynomial roots. An AR(p) process is a stationary process if and only if the modulus of all the roots of the AR characteristic polynomial are greater than one. An MA(q) process is always stationary if the MA coefficients are finite. An ARMA (p,q) model admits a unique stationary solution when the AR characteristic poly- nomial and the MA characteristic polynomial have no common roots and the AR polynomial satisfies that it has no unit roots. Use this information to determine which of the below models is stationary. (Make sure to justify your answer.) (a) VY + ²3 (Yt + 5Y₁-1) = € - €t-1 − −2+ 3…h.w/Find the compler exponential Fourir series Spectral frequency Sfer the Functions oFind the indicated series by the given operation. Show that by integrating term by term the expansion of - 2x the result is the expansion for In (1 - x2). 1- x2 1 S(-2x+ 2x3- 25+ 2x7 - .. ) da " x2 . (-2x + -..) dx = -x2 + x4 X° + Sex- 23. 25 - 2x7..) e x2 (2x- 2x3 + 2x5 - 2x7..) dx 2 1 1 x4 + w/ .. 1 S = x2. (-2x- 2x3 - 2x5 - 2x7 - ...) dx x4 S2x+ 2x3+ 25 + 2x7...) dx = x² + (2x + 2x + 2x5 + 2x7 +...) dx 1 x4 3 + X° +...Find the Fourier series representation of the periodic function below if c = 9 and d = 18.7. Then, find the value of an if n = 7. с -6Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. FreemanMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman