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Unformatted text preview: 6.042/18.062J Mathematics for Computer Science November 23, 2010 Tom Leighton and Marten van Dijk Problem Set 12 Problem 1. [15 points] In this problem, we will (hopefully) be making tons of money! Use your knowledge of probability and statistics to keep from going broke! Suppose the stock market contains N types of stocks, which can be modelled by independent random variables. Suppose furthermore that the behavior of these stocks is modelled by a double-or-nothing coin ip. That is, stock S i has half probability of doubling its value and half probability of going to 0. The stocks all cost a dollar, and you have N dollars. Say you only keep these stocks for one time-step (that is, at the end of this timestep, all stocks would have doubled in value or gone to 0). (a) [3 pts] What is your expected amount of money if you spend all your money on one stock? Your variance? (b) [3 pts] Suppose instead you diversified your purchases and bought N shares of all dif- ferent stocks. What is your expected amount of money then? Your variance? (c) [3 pts] The money that you have invested came from your financially conservative mother. As a result, your goals are much aligned with hers. Given this, which investment strategy should you take? (d) [3 pts] Now instead say that you make money on rolls of dice. Specifically, you play a game where you roll a standard six-sided dice, and get paid an amount (in dollars) equal to the number that comes up. What is your expected payoff? What is the variance?...
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- Fall '10
- Computer Science