You are trying to buy a stock at the best price. You need to buy it in the next 100 minutes. Every minute you will receive a random price (uniform distribution) that is a number between 1 and 100 dollars and decide whether to buy it or not.
1. Assuming you buy the stock in one trade, give a condition for buying the stock.
2. On average how many minutes will pass before that condition holds (expression or approximation is fine)?
3. If you could split up the trade, i.e, buy different amounts at different minutes, what would you do differently?
Update(Nov 17, 2010):
Solution posted by Sumit Somani (Senior Undergraduate, CSE, IITB) in comments! Same solution posted by me with spreadsheet in comments!