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 -5.56 x 10-4 + 5.56 x 10-6x, 4.44 x 10-3 – 4,44 x 10-6x, x E [100, 500] xE [500, 1000] otherwise f(x) = 0, Determine the following: а. Р(Х < 90) b. P(100 < X < 200) d. Value exceeded with probability 0.1. P(X > 800)
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 -5.56 x 10-4 + 5.56 x 10-6x, 4.44 x 10-3 – 4,44 x 10-6x, x E [100, 500] xE [500, 1000] otherwise f(x) = 0, Determine the following: а. Р(Х < 90) b. P(100 < X < 200) d. Value exceeded with probability 0.1. P(X > 800)
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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
-5.56 x 10-4 + 5.56 × 10-6x,
4.44 x 10-3 – 4,44 × 10-6x,
0,
х€[100, 500]
х€ 1500, 1000]
otherwise
f(x) =
Determine the following:
b. P(100 < X < 200)
а. Р(Х < 90)
с. Р(Х > 800)
d. Value exceeded with probability 0.1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3fa3e03-226c-4c92-b186-276760409442%2Fe7553022-6838-4840-a25e-ada3193ea538%2F2bg1zgj_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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
-5.56 x 10-4 + 5.56 × 10-6x,
4.44 x 10-3 – 4,44 × 10-6x,
0,
х€[100, 500]
х€ 1500, 1000]
otherwise
f(x) =
Determine the following:
b. P(100 < X < 200)
а. Р(Х < 90)
с. Р(Х > 800)
d. Value exceeded with probability 0.1.
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