you have $1000 and a certain commodity costs$2 an ounce. Suppose that after 1 week, there is a 50% that the commodity will cost $1 and a 50% that the commodity will cost$4.

i already know how to do the expected value of cash, but

(b) If your objective is to maximize the expected amount of commodity that you possess at the end of the week, what strategy should you employ?

my professor said setup a random variable Y. but he said the random variable Y represents the amount of commodity i buy today, but means, just buy 500 ounces of the commodity to maximize it.

he also hinted that this answer will involve E(g(x))