Interesting Simulation Problems....
- To: firstname.lastname@example.org
- Subject: [mg12084] Interesting Simulation Problems....
- From: LinLi Chee <email@example.com>
- Date: Sat, 25 Apr 1998 01:30:19 -0400
- Organization: UUNET Canada News Transport
Hi there, the following are some interesting simulation problems. Just wonder how i can do it with mathematica .... 1. Problem of Points Suppose there are two players and each player has an equal chance to win a round. The players agree to play 10 rounds for a pot of $100. After player A has won 5 rounds and player B has won 3 rounds, they are forced by unforeseen circumstances to stop. how should they then fairly divide the pot? (Use Simulation to solve) 2. Meeting Under the Clock (This problem is posed by Julian Simon(1994)) Two persons agree to arrive at the two clock sometime between 1 pm and 2 pm and to stay for 20 minutes. What is the probability that they will be there at the same time? 3. Aces Probelm (Warren Weaver got this wrong in the first edition of his book on probability) There are four players. A bridge hand is dealt and you state to the other three players that you have an ace. Find the probability, as calculated by someone else, whether or not you also have another ace. Later, you annouce that you have the Ace of Spades. What now is the probability that you have another ace? (also by simulation) 4. Beagle Problem (posed by Vos Savant) A shopkeeper says she has two new baby beagles for sale, but she does not know whether they are both male, both female, or a pair of male and female. You are only interested in the male. So she calls up the fellow who is giving them a bath and asks if at least one of them is a male. She then tells you that she has a male. What is the probability taht the other one is a male too? (simulation) 5. Bernoulli Test Bernoulli wanted to test whether the anglesof planes of the orbits of the known planets were randomly distributed. Modern data on the angles of the planets wrt the ecliptic are as follows: Mercury (7.00) , Venus (3.39), Mars (1.85), Jupiter (1.30), Saturn (2.49), Uranus (0.77), Neptune (1.77), Pluto (17.20). Develop two test of the null hypothesis that the planetary orbits are randomly distributed in space. Compute p-values via resampling. firstname.lastname@example.org