
Probability
You have $1000 and a certain commodity presently sells for $2 per ounce. Suppose that after one week the commodity will sell for either $1 or $4 an ounce, with these two possibilities being equally likely.
a) If your objective is to maximize the expected amount of money that you possess at the end of the week, what strategy should you employ?
b) If your objective is to maximize the expected amoung tof the commodity that you possess at the end of the week, what strategy should you employ?

It looks like you are going to have to propose some scenarios, because I think if you could answer this accurately you would be a stock market billionaire!
The obvious uncertainty is what will happen to the price during the week? Can it ever be more than $4 or less than $1? Do you have any more info on what the chances of it going low and than high are?
The simple cases are:
Buy nothing at all
Buy nothing until the end of the week
Spend all your money now and sell at the end of the week
Spend all your money now and keep commodity at the end of the week
To maximise money:
Buying now for $2 and selling at the end of the week gives an expected return of $1225 (50% chance of getting $2000, 50% of getting $500)
To maximise commodity:
Buy nothing until the end of the week. Then you will either be able to get 1000 ounces, or 250 ounces, with expected return of 625 ounces, better than buying now.
The complicated cases are to try to trade during the week, but I think that is beyond me!!

I calculated for the first one but I got a difference answer, should it be $1250?

Yup, i was just testing you ;)