Show complete and detailed solution. Do not shortcut. An article in Electric Power Systems Research ["Modeling Real-Time Balancing Power Demandsin Wind Power Systems Using Stochastic Differential Equations" (2010, Vol. 80 (8), pp. 966–974)]considered a new probabilistic model to balance power demand with large amounts of windpower. In this model, the power loss from shutdowns is assumed to have a triangular distributionwith probability density function[-5.56 × 10* +5.56× 10“x, xE[100,500]f(x)={ 4.44 x 10– 4.44× 10“x, xe[500,1000]0,otherwiseDetermine (in 6 decimal places):A. P (X < 90)B. P (100 < Xs 200)C. P (X > 800)D. Value exceeded with probability 0.1

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Answered: -5.56 x 10" + 5.56 × 10"x, xel100,500]…

Linear Algebra: A Modern Introduction

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ISBN:9781285463247

Author:David Poole

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Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

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4.1.8 An article in Electric Power Systems Research ["Model- ing Real-Time Balancing Power Demands in Wind Power Sys- tems Using Stochastic Differential Equations" (2010, Vol. 80(8), pp. 966-974)] considered a new probabilistic model to balance power demand with large amounts of wind power. In this model, the power loss from shutdowns is assumed to have a triangular distribution with probability density function f(x) = -5.56 × 10-4 +5.56 × 10-6x, 4.44 x 10-³-4.44 × 10-6x, 0, { x = [100, 500] x € [500, 1000] otherwise Determine the following: a. P(X 800) d. Value exceeded with probability 0.1.
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-5.56 x 10" + 5.56 × 10"x, xel100,500] S(x) ={ 4.44 x 10 - 4.44 × 10“x, xe[500,1000] 0, otherwise Determine (in 6 decimal places): A. P (X < 90) B. P (100 800)