A random process x(t) is applied to a network with impulse response h(t) u(t) texp (- bt) where b>0 is a constant. The cross-correlation of x(t) with the outputy(t) is known to have the same form.Rxx(t) = u(t) T exp (– bt)(a) Find the auto correlation of y(t) ?(b) What is the average power in y(t) ?

Answered: Image /qna-images/answer/1f4d338b-b8eb-4692-99db-5d4ced9603ec.jpg

Answered: A random process x(t) is applied to a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Calculate the residual of P = (1.2, 2.4) with respect to the line 3x + 4y = 12.
5
Look at the following regression table where the dependent variable is the demand for illegal massage services in a city in the United States. Specifically, the dependent variable is the number of customers per hour (Models 1 and 2) or per day (Models 3 and 4). (a) Explain why the coefficient for Population/1,000 in Model 2 is very different from the one in Model 4?(b) Can you reject H0 in Model 1 if H0 : βP opulation/1,000 = 0.01, H1 : βPopulation/1,000 6= 0.01, and α = 0.01?
A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 8 children from her practice, measures their height and head circumference, and obtains the data shown in the table. Complete parts (a) through (e) to the right. Height (in.) Head Circumference (in.) O 27 17.4 Data Table 25.5 17.2 26 17.2 25.75 17 Critical Values for Correlation Coefficient 27.75 17.5 26.5 17.2 26.25 17.2 3 0.997 26.75 17.4 4 0.950 0.878 Click here to see the Table of Critical Values for Correlation Coefficient. 0.811 7 0.754 0.707 0.666 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374 29 0.367 30 0.361
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 =
Consider the linear regression y, = B, + Bx, + u;, i=1,...,n,n+1,..,n+ p where E(u,) = 0. Is it possible to observe a result that E(B,)+ B,, while E(B) = B,-
Heteroscedasticity Stigler and Friedland (1983) conducted a study to determine whether the separation of company control from company ownership affects company profits. Using data from 69 companies in the United States, the authors estimate the following model: profiti = α + β1asseti + β2management_controli + ei Where i is company and: profiti = annual profit (in million dollar) asseti = company asset (in million dollar) management_controli = dummy variable that is worth one if the control of the company is held by the manager The regression results are presented in the table in the picture a. Explain whether the statements below are TRUE, FALSE, or CANNOT BE DETERMINED. "If there is a heteroscedasticity problem, the confidence interval of the OLS estimator is not valid." b. Determine the 95% confidence interval for the parameter 2, what can you conclude?
Derive the least squares estimator of Bo for model Y₁ = P + Ei the re regression
A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = B, + B,x + E where y = traffic flow in vehicles per hour x = vehicle speed in miles per hour. The following data were collected during rush hour for six highways leading out of the city. Traffic Flow (y) Vehicle Speed (x) 1,257 35 1,329 40 1,227 30 1,335 45 1,351 50 1,123 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ý = bo + b,x + b,x? (a) Develop an estimated regression equation for the data of the form ý = b, + b,x + b,x2. (Round b, to the nearest integer and b, to two decimal places and b, to three decimal places.)
y 6. For this problem, use a linear regression model. 1 2 12 a) Use the correlation formula to the right to calculate the correlation R - 1 Sx Sy 11 п-1 n 8 14 SSR = 1 SST SSE 11 17 Coefficient of Deternination → R2 SST 14 16 b) Find R^2 using SSR/SST SST = v- 7)² Sum of Squares Total → 17 20 19 24 Sum of Squares Regression → SSR = 20 22 SSE = >v-y)? Sum of Squares Error → 25 27 c) Find the slope using the formula to the right -- Σ-3-) Slope a= d) Verify your answers to parts a,b,c using another method of your choice intercept b= y-ax where overbar denotes average e). Find the residual for x = 14 f) Use your regression equation to find the probable x-value for y = 83, you may round your answer to 2 decimal places. %3D
45. Calculate the correlation coefficient from the following results : N- 10, Σ X= 350 Σ Υ- 310 Σ (X-35= 162, Σ (Y- 31)? = 222 E (X-35) (Y-31) = 92. erlw %3D %3D Also find the regression line of Y on X

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