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 positive? Round your answer to two decimal places (e.g., 98.8)

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 positive? Round your answer to two decimal places (e.g., 98.8)

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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5. A test of hypothesis has the following details: HO : u = 250 vs Ha : u f= 250, n = 36, 02 = 324, a = 0.03, x = 244, the data is normally distributed. What is the p-value and the correct decision for this test? (a) p-value = 0.0228, Reject HO (b) p-value = 0.0456, Reject HO (c) p-value = 0.0228, Do not reject HO (d) p-value = 0.0456, Do not reject HO %3D
1) Below are data of foam indexes for three different espresso makers. Test the hypothesis that foam indexes differ between the three. (Note: these data are highly kurtotic, so normality cannot be assumed.) Set a at 0.05. Which test should you use and why? State the hypothesis, provide the critical value and test statistic and state your conclusions. Hyper-Espresso Method (HIP) I-Espresso System (IT) 56.19 Bar Machine (BM) 36.64 70.84 39.65 46.68 36.67 35.35 40.11 37.74 73.19 35.96 57.78 38.52 48.61 33.52 37.12 37.33 72.77 21.02 24.81 65.04 32.68 48.33 34.18 62.53 23.08 54.26
3. A certain actuarial model of mortality rate is fitted to some given data. Table 2 below reports the Z-score statistic of the model graduation. (a) List the key steps involved in developing an actuarial model. (b) Explain why we need graduation. What do we actually test statistically? (c) What are the drawbacks of a x²- test? Explain how the sign test may overcome these. (d) Write a statistical hypothesis to test the adherence of the model to the data. (e) The life table data below provides an estimate of mortality rates obtained from a three-parameter Poisson model. Give the quality of goodness-of-fit of the Poisson model by performing statistical tests based on:, and draw the conclusions. i. x²-test. ii. Standardized deviations test. [Consider the following subintervals for the data range: A₁ = (-∞, −3], A₂ = (−3,−2], A3 = (−2, −1], A4 = (–1, 0], A5 = (0, 1], A6 = (1, 2], A7 = (2, 3], and Ag = (3, ∞).] iii. Sign test iv. Change-of-sign test v. Grouping-of-sign test vi. Lag-2 serial…
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16. A scatterplot of the monthly salary (in thousands of pesos) versus years of education for seven full-time workers is displayed below. The least- squares regression line is drawn on the plot. Six of the data points are plotted with open circles and the seventh is plotted with a solid circle. The data point plotted with a solid circle to 20 Ne stynan eftdutatien A. has a large residual and is influential. B. has a small residual and is influential. C. has a large residual and is not infiluential. D. has a small residual and is not influential. 00 09 oad jo umroy s
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
Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and 1.6 GPa, respectively (values given in the article "Influence of Material Properties Variability on Springback and Thinning in Sheet Stamping Processes: A Stochastic Analysis" (Intl. J. of Advanced Manuf. Tech., 2010: 117-134)). (a) If X is the sample mean Young's modulus for a random sample of n = 64 sheets, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution? E(X) ох = GPa GPa (b) Answer the questions posed in part (a) for a sample size of n = 256 sheets. E(X) GPa GPa ох = (c) For which of the two random samples, the one of part (a) or the one of part (b), is X more likely to be within 1 GPa of 70 GPa? Explain your reasoning. O X is more likely to be within 1 GPa of the mean in part (b). This is due to the increased variability of X that…
Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and 1.6 GPa, respectively (values given in the article "Influence of Material Properties Variability on Springback and Thinning in Sheet Stamping Processes: A Stochastic Analysis" (Intl. J. of Advanced Manuf. Tech., 2010: 117-134)). (a) If X is the sample mean Young's modulus for a random sample of n = 16 sheets, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution? E(X) = GPa GPa x = (b) Answer the questions posed in part (a) for a sample size of n = 64 sheets. E(X) GPa GPa ox = (c) For which of the two random samples, the one of part (a) or the one of part (b), is X more likely to be within 1 GPa of 70 GPa? Explain your reasoning. O X is more likely to be within 1 GPa of the mean in part (b). This is due to the decreased variability of X that…
Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and 1.6 GPa, respectively (values given in the article "Influence of Material Properties Variability on Springback and Thinning in Sheet Stamping Processes: A Stochastic Analysis" (Intl. J. of Advanced Manuf. Tech., 2010: 117-134)). | If X is the sample mean Young's modulus for a random sample of n = 64 sheets, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution? EX) = GPa GPa J Answer the questions posed in part (a) for a sample size of n = 256 sheets. E(X) = GPa GPa For which of the two random samples, the one part (a) or the one of part (b), is X more likely to be within 1 GPa of 70 GPa? Explain your reasoning. O X is more likely to be within 1 GPa of the mean in part (b). This is due to the increased variability of X that comes with a larger…
Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and 1.6 GPa, respectively (values given in the article "Influence of Material Properties Variability on Springback and Thinning in Sheet Stamping Processes: A Stochastic Analysis" (Intl. J. of Advanced Manuf. Tech., 2010: 117–134)). (a) If X is the sample mean Young's modulus for a random sample of n = 64 sheets, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution? E(X) = GPa ? X = GPa (b) Answer the questions posed in part (a) for a sample size of n = 256 sheets. E(X) = GPa ? X = GPa
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).
In a White test for heteroskedasticity, what is the degrees of freedom? The number of explanatory variables in the auxiliary regression + 1 The number of explanatory variables in the initial model + 1 The number of explanatory variables in the auxiliary regression The number of explanatory variables in the initial model