Hey BuddhsNZ.

You should start by setting up a value function based on the random variables.

So think about a value function that is a function of your random variables [something like V = f(X,Y,Z)]

Now if you take the expectation of this, you will get E[V] = E[f(X,Y,Z)] and if you have coeffecients and other information that are independent of X, Y, Z (for example V = aX + bY + cZ has coeffecient variables a,b,c independent of X,Y,Z random variables), then what will happen is you will get a deterministic relationship between other variables and the expectations of the random variables.

You can then look at where this gets maximized with respect to your other information to figure out what f(X,Y,Z) should be and hence that becomes your value function.