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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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
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