Expectation of a continuous uniform distribution function of a random variable- university question

Question

I have that the expected value will be $$\int_0^{200}f(x)g(x)\mathrm dx$$ where g(x) is the profit function, but I am unsure what to actually substitute g(x) for.

Any help would be very much appreciated.

Answer 1

The profit has been given to you:

$$g(x) = \begin{cases}x-0.5(n-x) &, x \le n \\ n-5(x-n)&, x >n \end{cases}$$

Upon evaluating the expectation, it can be expressed in terms of $n$.