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Question: An article in Electric Power Systems Research considered a new probabilistic model to balance pow...

An article in Electric Power Systems Research 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^ -6)* x , for x in [100, 500]

(4.44 * 10^-3) - (4.44 * 10^-6)* x , for x in [500, 1000]

0, otherwise

(a) Determine the cumulative distribution function for the random variable. Use the cumulative distribution function to determine the probability that 400<X<500.

(b) Determine the mean and variance of the random variable X.

Answer 1