Question

A company operates a solar installation in the desert in Western Australia. It is reviewing its operating practices with a view to making them more efficient.

a) The solar installation generates electric power from sunlight and incurs operating costs for cleaning the solar modules (sometimes called solar panels) and replacing solar modules that have failed. The annual revenue from the electric power is variable due to variable cloudiness and solar module failure and has a mean of $2.78m and a standard deviation of $0.32m. The annual operating costs have a mean of $0.51 and a standard deviation of $0.12m.

Calculate the mean and standard deviation of the annual profit = annual revenue – annual operating costs.

Answer 1

Let X denote Annual Revenue

Therefore, E(X) is Mean Value of X i.e $ 2.78 mn and of X is $ 0.32 mn

Let Y denote Annual Operating Cost

Therefore, E(Y) is Mean Value of Y i.e $ 0.51 mn and of Y is $ 0.12 mn

Profit = Revenue - Operating Costs

X & Y are independent variables.

Let P denote Annual Profit, therefore P = X-Y

We are looking for

1) Mean Annual Profit - E(P) = E(X-Y) = E(X) - E(Y) = $ 2.78 mn - $ 0.51 = $ 2.27 mn

2) Standard Deviation of Annual Profit - (P) = Square root of the sum of the squared values of X & Y = (0.32)² + (0.12)²

^{= 0.1024 + 0.0144 = 0.1168}

^{= 0.34176}

Therefore Mean Annual Profit is $ 2.27 mn and Standard Deviation Annual Profit is $ 0.34176 mn