Question 1. (12) Westminster Energy, a state monopoly, is considering building a new power plant in the new industrial zone. The director evaluates the feasibility of medium-scale and large scale plants by assessing the expected profit and risk involved. The demand for energy is generally classified as high, medium, and low over a year and the forecasted profit over the seasons are x and y for each plant scale are summarized as follows: Demand Probability Medium-scale Large-scale Profit (x) (in '000) Profit (v) (in '000) Low 0.2 30 Medium 0.5 60 50 High 0.3 100 130 40 (a) Calculate the expected profit for both medium-scale and large-scale power plant. Explain to the director which plant scale is desirable. Show your working carefully. (3) (b) Calculate the variance and standard deviation of the profit for each plant scale. What is your recommendation? Show your working carefully. (5) c) Calculate the coefficient of variation for each of the plant scale. How would your recommendation change? Explain