Consider the difference equation (with initial conditions y(-1), y(-2) provided below in the data)(n 20 and integer. Note: 6(n) is the unit impulse sample.):y(n) = ay(n – 1) – by(n – 2) +6(n)1. Is the solution to this equation for n >0 stable ? Answer with reason(s).2. What is the value of y(7) and limn-00 y(n) in the solution for y(n)Data: [y(-2), y(-1), a, b] = [-2.0, –-1.0,0.32, 0.2244]

Consider the provided question, Given, yn=ayn-1-byn-2+δn where, δn is the unit impulse sample. The…

Consider the difference equation (with initial conditions y(-1), y(-2) provided below in the data) (n > 0 and integer. Note: 8(n) is the unit impulse sample.): y(n) = ay(n – 1) – by(n – 2) + d(n) 1. Is the solution to this equation for n >0 stable ? Answer with reason(s). 2. What is the value of y(7) and limn-+0 y(n) in the solution for y(n) Data: [y(-2), y(-1), a, b] = [-2.0, –1.0, 0.32, 0.2244]

Consider the difference equation (with initial conditions y(-1), y(-2) provided below in the data) (n > 0 and integer. Note: 8(n) is the unit impulse sample.): y(n) = ay(n – 1) – by(n – 2) + d(n) 1. Is the solution to this equation for n >0 stable ? Answer with reason(s). 2. What is the value of y(7) and limn-+0 y(n) in the solution for y(n) Data: [y(-2), y(-1), a, b] = [-2.0, –1.0, 0.32, 0.2244]

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question 2. Show that, for a simple linear regression, R² = ry, where R² is the coefficient of determination and rxy is the sample correlation between Y and X. Hint: Σ" (Υ - Y)2 Σ1(Y₁-Y)²¹ SxY √SXXSYY' where Sxy = 1 (X; — X)(Y; — Y), Sxx = ₁1(X; - X)², Syy = ₁₁(Y₁ - Y)². R² = "XY =
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(b) For a given set of trivariate data, the following results were obtained: X = 53, Y = 28, 6 (Y on X) =- 1.5, d (X on Y)=- 0.2. Find : (i) The two regression equations. (ii) the coefficient of correlation. (iii) The most probable value of Y when X=60.
D. Only OLS assumption #2 is satisfied. The estimated regression is Y = 39+0.45X; Compute the estimated regression's prediction for the average score of students given 99, 129, or 155 minutes to complete the exam. Given 99 minutes, the estimated regression's prediction for the average score of students is Given 129 minutes, the estimated regression's prediction for the average score of students is Given 155 minutes, the estimated regression's prediction for the average score of students is (Round your responses to two decimal places.) Compute the estimated gain in score for a student who is given an additional 19 minutes on the exam. The estimated gain in score for a student who is given an additional 19 minutes on the exam is (Round your response to two decimal places.) Click to select your answer(s). W (DELL] o search PROU II
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4. Suppose that n=100 i.i.d observations for (Y₁, X₁) yield the following results Ỹ = 32.1 +66.8X, SER=15.1, R² = 0.81 (15.1) (12.2) Another researcher is interested in the same regression, but he makes an error when he enters the data in his regression program: He enters each observation twice, so he has 200 observations. Using these 200 observations, what results will be produced by his program? Write it in the following format: Ỹ +---X, SER= (---) (---) R² =
Q8. (i) Suppose the manufacturer of a new drug wants to test H,: 0 = 0.8 versus H,: 0 = 0.6 where 0 is true proportion of patients cured by the drug. His test statistic is x, the number of successes (cures) in n = 20 trials, and he will accept Ho if x >16; otherwise he will reject it. Find a and ß. (ii) Now suppose we wish to test Ho: 0 2 0.8 versus H;: 0 < 0.8. Using some selective values of 0 [ eg 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9] to make a table of the Probabilities of type I error, type II error and the power function [Probability of rejecting Ho]. Use the table draw a plot of the power function 1(8).
Use the following linear regression equation to answer the questions. x1 = 2.0 + 3.6x2 – 7.8x3 + 2.1x4 a) Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1?b) Suppose x2 increased by 2 units. What would be the expected change in x1?c) Suppose x2 decreased by 4 units. What would be the expected change in x1?
Suppose that n= 195 I.I.d. observations for (Y, X;) yleld the following regression results: v= 32.68 + 67.55Xx, SER= 18.63, R = 0.84 (15.7) (12.5) Another researcher is interested in the same regression, but he makes an error when he enters the data into the regression: He enters each observation twice, so he has 390 observations (with observation 1 entered twice, observation 2 entered twice, and so forth). Which of the following eatimated parameters change result? (Check all that apply) O A. The estimated intercept and slope. O B. The R of the regression. Yc. The standard error of the regrussion (SER). YD. The standard errors of the estimated coefficients. Using the 390 observations, what results will be produced by his regression program? Ý= 32.68 + 67.55X, SER =.R = 0.84 (Round your responses to two decimal places)
Q4. In simulation study of a manufacturing system, both the average daily production rates obtained from simulation model (use data from day n1/2 to day n2/2, round it to nearest integer) and from the real system are given, in data set 3. - n1= 27.6. n2=97.6 - Apply t test to decide if we can assume the simulation model is a valid representation of the real system is given. - Check if we can assume the average daily production rates obtained from simulation in successive days are independent by using scatter diagram (X Y plot in excel; X axis Xi value Y axis Xi+1)
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