The increase in demand for electric power in millions of kilowatt hours over the next 2...

  

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The increase in demand for electric power in millions of kilowatt hours over the next 2 years in a certain area is a random variable X with density f(z) = 2*/64,0 < z 4. Assume f(x) = 0 elsewhere. (a) (5 points) Why is this a legitimate density? (b) (10 points) Find E(X) and Var(X). (c) (5 points) The area only has the capacity to generate an additional 3 million kilowatt hours. What is the probability that demand will exceed supply? (d) (5 points) Suppose in another area the increase in demand for electric power is Y = 2.5X. Calculate the expected combined increase in demand for electric power across both areas and the variance of the this combined demand. The increase in demand for electric power in millions of kilowatt hours over the next 2 years in a certain area is a random variable X with density f(z) = 2*/64,0 < z 4. Assume f(x) = 0 elsewhere. (a) (5 points) Why is this a legitimate density? (b) (10 points) Find E(X) and Var(X). (c) (5 points) The area only has the capacity to generate an additional 3 million kilowatt hours. What is the probability that demand will exceed supply? (d) (5 points) Suppose in another area the increase in demand for electric power is Y = 2.5X. Calculate the expected combined increase in demand for electric power across both areas and the variance of the this combined demand.