19. An article in International Journal of Electrical Power & Energy Systems "Stochastic Optimal Load Flow Using a Combined Quasi-Newton and Conjugate Gradient Technique" (1989, Vol. 11(2), pp. 85-93) considered the problem of optimal power flow in electric power systems and included the effects of uncertain variables in the problem formulation. The method treats the system power demand as a normal random variable with 0 mean and unit variance. What is the probability that the power demand is greater than -2 and less than 2?

19. An article in International Journal of Electrical Power & Energy Systems "Stochastic Optimal Load Flow Using a Combined Quasi-Newton and Conjugate Gradient Technique" (1989, Vol. 11(2), pp. 85-93) considered the problem of optimal power flow in electric power systems and included the effects of uncertain variables in the problem formulation. The method treats the system power demand as a normal random variable with 0 mean and unit variance. What is the probability that the power demand is greater than -2 and less than 2?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Q.4-134
An article in Technometrics ["Validation of Regression Models: Methods and Examples" (1977, Vol. 19(4), p. 425)] presented the following data on the motor fuel octane ratings of several blends of gasoline: 88.5 98.8 89.6 92.2 92.7 88.4 87.5 90.9 94.7 88.3 90.4 83.4 87.9 92.6 87.8 89.9 84.3 90.4 91.6 91.0 93.0 93.7 88.3 91.8 90.1 91.2 90.7 88.2 94.4 96.5 89.2 89.7 89.0 90.6 88.6 88.5 90.4 84.3 92.3 92.2 89.8 92.2 88.3 93.3 91.2 93.2 88.9 91.6 87.7 94.2 87.4 86.7 88.6 89.8 90.3 91.1 85.3 91.1 94.2 88.7 92.7 90.0 86.7 90.1 90.5 90.8 92.7 93.3 91.5 93.4 89.3 100.3 90.1 89.3 86.7 89.9 96.1 91.1 87.6 91.8 91.0 91.0 Construct a stem-and-leaf display for these data. Calculate the median and quartiles of these data.
(c) Randomization is used to (i) measure the random (unexplained) variability.(ii) balance the effects of hidden variables.(iii) control the effects of known controllable factors of no interest to the experimenter. (iv) be able to run the experiment. (d) Blocking is used to (i) measure the random (unexplained) variability.(ii) balance the effects of hidden variables.(iii) control the effects of known controllable factors of no interest to the experimenter. (iv) be able to run the experiment. (e) Replication is used to(i) measure the random (unexplained) variability.(ii) balance the effects of hidden variables.(v) control the effects of known controllable factors of no interest to the experimenter. (vi) be able to run the experiment.
lecturer would like to know if the foundation Cumulative Grade Point Average (CGPA) predicts the undergraduate CGPA of engineering students at year one. She obtained the relevant information from 105 randomly selected students as follows: Σy = 333.15, Σxy = 1043.626, = 1021.487, > y² = 1077.836 %| Σ %3D (i) Obtain the least square regression line, ŷ = a + bx for the study. (ii) Estimate the strength of the association between the foundation CGPA and CGPA in year one. Interpret the result.
12. The OLS estimators of the coefficients in a multivariate linear regression model will be unbiased and consistent if the following set of conditions holds A. expected value of the error term given the independent variables is zero, the variance of the error term does not depend on the values of the independent variables, the observations (Yi,Xi,1,X₁,2,...,Xik) are i.i.d., large outliers are unlikely B. expected value of the error term given the independent variables is zero, the variance of the error term does not depend on the values of the independent variables, there is no perfect multicollinearity between the independent variables, the observations (Y₁X₁,1X₁,2,...,Xik) are i.i.d. C. expected value of the error term given the independent variables is zero, there is no perfect multicollinearity between the independent variables, the observations (Yi,Xi,1,Xi,2,...,Xik) are i.i.d., large outliers are unlikely D. the variance of the error term does not depend on the values of the…
True or False: In a model with an interaction variable, we can drop the interaction term if its pvalue>.05
5
An article in International Journal of Electrical Power & Energy Systems {"Stochastic Optimal Load Flow Using a Combined Quasi- Newton and Conjugate Gradient Technique" (1989, Vol. 11(2), pp. 85-93)} considered the problem of optimal power flow in electric power systems and included the effects of uncertain variables in the problem formulation. The method treats the system power demand as a normal random variable with 0 mean and unit variance. What is the power demand value that is exceeded with 8096 probability? Round your answer to two decimal places (e.g. 98.76). Ancwor ic Rlanlk 1
2. In building an arena, steel bars with a mean ultimate tensile strength of 400 Megapascal (MPa) with a variance of 81 MPa were delivered by the manufacturer. The project engineer tested 50 steel bars and found out that the mean ultimate tensile strength is 390 MPa. The decision for the extension of the contract with the manufacturer depends on the engineer. Test the hypothesis whether there is no significant difference between the two means using a two - tailed with a = 0.01.
Anarticle in Technometrics by S. C. Narula and J. F. Wallington Prediction, Linsar Regression, anda Minimum Sum of Relative Erro Vol. 19, 1977) presents data on the selling price (y) and annual taxes (x) for 24 houses. The taxes include local, school and county ta The data are shown in the following table. Sale Price/1000 Taxas/1000 25.9 4.9176 29.5 5.0208 27.9 4.5429 25.9 4.5573 29.9 5.0597 29.9 3.8910 30.9 5.8980 28.9 5.6039 35.9 5.8282 315 5.3003 31.0 6.2712 30.9 5.9592 30.0 5.0500 36.9 8.2464 419 6.6969 40.5 7.7841 43.9 9.0384 37.5 5.9894 37.9 7.5422 44.5 8.7951 37.9 6.0831 38.9 8.3607 36.9 8.1400 45.8 9.1416
9) The following results are from a regression where the dependent variable is GRADUATION RATE and the independent variables are % OF CLASSES UNDER 20, % OF CLASSES OF 50 OR MORE, STUDENT/FACULTY RATIO, ACCEPTANCE RATE, 1ST YEAR STUDENTS IN TOP 10% OF HS CLASS. The data were split into 2 samples and the following regression results were obtained from the split data. c) Based on a comparison of the two sets of output, does it appear that there is heteroscedasticity in the data set? Explain. Be sure to write down your null and alternative hypothesis, calculate the test statistic, and find your critical value (test at the 5% level of significance).