1.8 An article in tric Power Systems Resea [Model- Real-Time Balancing Power Demands in Wind Power Sys- ns Using Stochastic Differential Equations" (2010, Vol. 80(8), . 966–974)] considered a new probabilistic model to balance wer demand with large amounts of wind power. In this model, power loss from shutdowns is assumed to have a triangular tribution with probability density function (x) = { -5.56 × 10-4 +5.56 × 10-6x, 4.44 x 10-³-4.44 × 10-6x, 0, termine the following: a. P(X <90) S. P(X > 800) x = [100, 500] x = [500, 1000] otherwise b. P(100 < X ≤ 200) d. Value exceeded with probability 0.1.
1.8 An article in tric Power Systems Resea [Model- Real-Time Balancing Power Demands in Wind Power Sys- ns Using Stochastic Differential Equations" (2010, Vol. 80(8), . 966–974)] considered a new probabilistic model to balance wer demand with large amounts of wind power. In this model, power loss from shutdowns is assumed to have a triangular tribution with probability density function (x) = { -5.56 × 10-4 +5.56 × 10-6x, 4.44 x 10-³-4.44 × 10-6x, 0, termine the following: a. P(X <90) S. P(X > 800) x = [100, 500] x = [500, 1000] otherwise b. P(100 < X ≤ 200) d. Value exceeded with probability 0.1.
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Chapter1: Combinatorial Analysis
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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 <90) b. P(100 < X < 200)
c. P(X> 800) d. Value exceeded with probability 0.1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7640db3-da2d-40b9-97ee-6a106396ec94%2F94e2b241-1546-4a98-88d0-7bae95602559%2Fxtjdok_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
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 <90) b. P(100 < X < 200)
c. P(X> 800) d. Value exceeded with probability 0.1.
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