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. 966974)]

An article in Electric Power Systems Research [€œModeling 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

Determine the following:

(a) P(X < 90)

(b) P(100 < X ‰¤ 200)

(c) P(X > 800)

(d) Value exceeded with probability 0.1.

[-5.56 x 104 +5.56x 10x, 4.44 10x, f(x) = { 4.44 x 10 0, xE[100,500] xe[500,1000] otherwise