An article in Electric Power Systems Research ["Modeling Real-Time Balancing Power Demands in Wind Power Systems Using Stochastic Differential Equations" (2010, Vol. 80 (8), pp. 966–974)] considered a...

Show complete and detailed solution. Do not shortcut.

800) D. Value exceeded with probability 0.1 "/>
Extracted text: An article in Electric Power Systems Research ["Modeling Real-Time Balancing Power Demands in 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 wind power. In this model, the power loss from shutdowns is assumed to have a triangular distribution with 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, otherwise Determine (in 6 decimal places): A. P (X < 90)="" b.="" p="" (100="">< xs="" 200)="" c.="" p="" (x=""> 800) D. Value exceeded with probability 0.1