3.14 Consider each of the following models: (i) (1 B)Z, (1 1.5B)a, (ii) (1 .8B)Z (iii...
Problem 1 Put each of the following models, (a) X1 Z,-1.3.1 +0.4.2, t-lt (c) X.9X,-1-0.88X,-2+Z,+0.2+0.7Z-2 in the form using the backward shift operator B and determine whether the model is causal and/or invertible.
Question 1 Which of the following hydrogens is the most acidic? II IV I III A. IV B. V C. III D.I E. II Question 2 What is the product, Z, of the following reaction sequence? iz H30+ T-H20)* ia. CI H307 + Z مل I II III IV A. IV B. II C. III D.V E.
2. (a) Consider the following process: where {Z) is a white noise process with unit variance. [1 mark] ii. Find the infinite moving average representation of X,i.e., find the scquence [6 marks] i. Explain why the process is stationary. (6) such that Xt = Σ b,2-j. iii. Calculate the mean and the autocovariance "Yo, γι and 72 of the process. 7 marks iv. Given 40 = 0.1 and Xo = 1.8, find the 2-step ahead forecast of the time series...
(b) In each case below, state whether the statement is true or false. Justify your answer in each case. (i) A+B is an invertible 2×2 matrix for all invertible 2×2 matrices A, B. [4 marks] (ii) If A is an n×n invertible matrix and AB is an n×n invertible matrix, then B is an n × n invertible matrix, for all natural numbers n. [4 marks] (iii) det(A) = 1 for all invertible matrices A that satisfy A = A2....
3. For each of the following discrete-time sequences: (i) Find the Z-transform (ZT), if it exists, and plot the region of convergence (ROC) in the Z-plane (ii) Find the poles and zeros and plot them in the 2-plane (iii) Determine whether the DTFT of the sequence exists (a) x[n] = 8[n – 1] + 28[n – 3] (b) [n] = (0.9e-j*)" u[n + 2] – 2-ul-n - 1] (c) x[n] = 2-" un + 1]
Name: 1 What is the major product of the following reaction? (CHдЬсo (CHЊ,сон Br IV A) I B) II C) III D) IV 2. What is the major elimination product obtained from the following reaction? NaOMe MeOH Br IV A) I B) II C) III D) IV 3. Which of the following is the most reactive substrate in an E2 reaction? CHiCH(Br)CH2CHs (CHs)sCBr CH3Br CH3CH2CH2CH2Br п ш IV I B) II С) ш D) IV A) I 4 Which of...
(1) Consider the following sample of gases: = He Z (iii) If the three samples are all at the same temperature, rank them with respect to (a) total pressure; (b) partial pressure of helium; (c) density; (d) average kinetic energy of particles. (II) The temperature of a gas is raised from 10 °C to 20 °C. Will the volume double if mass and pressure do not change? Why or why not? (Show your calculations) (III) If 3.25 L of gas...
Edit SECTION B ATTEMPT ALL 1 Define the following terms. (1 mark each) 1 Concept II Paradigm III. Assumptions IV Conceptual framework V Theories 5 marks 2 Discuss five (5) importance of nursing theories. (10 marks) 3. Briefly discuss five (5) characteristics of nursing theories (10 marks) 4 (a) Discuss how Virginia Henderson theory influence nursing practice today. (5 marks) 5 (b) state and explain four characteristics of nursing theories (8 marks) 6 (a) State and explain four phases in...
(a) Given the following periodic signal a(t) a(t) -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 i. [2%) Determine the fundamental period T ii. [5%] Derive the Fourier series coefficients of x(t). iii. [396] Calculate the total average power of z(t). iv. [5%] If z(t) is passed through a low-pass filter and the power loss of the output signal should be optimized to be less than 5%, what should be the requirement of cutoff frequency of the low-pass filter?...
For Questions 1, consider the following classifications: Feasible Region I- Finite Line Segment II -Non-existent III - Polygon IV-Single Point V - Unbounded Optimal Solution A -Alternate Optima B-No feasible solution C- Unbounded D-Unique 1. Suppose an LP with 5 regular constraints (other than the non-negativity constraints) has "lr as its feasible region. If a new constraint is added, which of the following CANNOT be the type of the new optimal solution? a, A b. В с. С d. De,...