Question

Determine the mean and variance of the random variable:

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
f (x) =

−5.56 × 10^−4 + 5.56 × 10−^6x, x ∈ [100, 500]
4.44 × 10^−3 − 4.44 × 10^−6x,    x ∈ [500, 1000]
0, otherwise

Answer 1

GIVEN THAT

An article in Electric Power Systems Rearch ["Modeling Real-Tme Power Demands in Wind Power Systems Using Stochastic Differential Equations"(2010 ,Vol.80(8),pp,966-974]