Consider the following time series data

Problem 15-05 (Algorithmic) Consider the following time series data. Week 1 2 3 4 5 6 Value 19 14 17 12 17 14 a. Choose the correct time series plot. (1) (iI) 20 Time Series Value 20 Time Series Value 16 16 14 14 12 12 10 10 Weck(t) Week(!) (Til) (iv) Time Series Value 20 Time Series Value 16 16 14 14 12 10 10 Week(t) Week(!) What type of pattern exists in the data?1. True III Variables with zero covariance are always independent li. False C. dependent random variables are always correlated i. True ii. False d. uncorrelated random variables are always independent i. True li. False e. For the bivariate (X & Y) if E[XY] = 0, the bivariate is independent i. True li. False f. Orthogonal random variables are always uncorrelated. i. True ii. False g. If Y = X[1 - X where X is a uniformly distributed random variable over the interval (0, 1), then E[ Y] = 1/12. i. True ii. False(1 mark each) For each of the given matrices, select all decompositions that can be applied to it. You do not have to show your work for this question. 2 ) A = 6 1 O Diagonalization (i.e., A = PDP-1 with D diagonal) O Schur triangularization O Spectral decomposition O Singular value decomposition b) B = 0 1.001 Diagonalization O Schur triangularization O Spectral decomposition O Singular value decomposition c) C is the 75 x 75 matrix with every entry equal to 1. Diagonalization Schur triangularization O Spectral decomposition Singular value decomposition d) D = 0 1 1 Diagonalization Schur triangularization Spectral decomposition Singular value decomposition