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Three players enter a room and are given a red or a blue hat to wear. The color of each hat is determined by a fair coin-toss. Players cannot see the color of their own hats, but do see the color of the other two players' hats. The game is won when at least one of the players correctly guesses the color of his own hat and no player gives an incorrect answer. In addition to having the opportunity to guess a color, players may also pass. Communication of any kind between players is not permissible after they have been given hats; however, they may agree on a group strategy beforehand. Verify that there is a group strategy that results in a 3/4 probability of winning. (This puzzle was discussed in the New York Times of April 10, 2001. The hat problem with many players is related to problems in coding theory. The strategy gets far more complicated for larger numbers of players. In the game with 2m - 1 players, there is a strategy for which the group is victorious with a probability of (2m - 1)/2m).
A digital communications system consists of a transmitter and a receiver During each short transmission interval the transmitter sends a signal.
a recent study focused on the amount of money single men and women saved monthly. the information is summarized below.
If he were to conduct a second study to reduce the maximum error of estimate to 6, about how many hard drives should he include in his new sample?
Using alpha = 0.05 and a computed value of +4.49, can we conclude that the percentage of claims for married policyholders is less then for single policyholders?
chicago ohare and atlanta hartsfield-jackson are the two busiest airports in the unitedstates. the congestion often
in january 2007 consumer reports published their study of bacterial contamination of chicken sold in the u.s. they
Let x denote the distance from the lower left-hand corner A of the square to the selected point. What are possible values of x? Is x a discrete or a continuous variable?
Write a MATLAB program to calculate the probability if is a Gaussian random variable for an arbitrary a and b > 0 Note you will have to specify the mean and variance of the Gaussian random variable.
Merger. Explain why the facts you know about variances of independent random variables might encourage two small insurance companies to merge.
a company buys components from three suppliers. they get 50 from supplier 1 20 from supplier 2 and the rest from
1.an experiment was carried out to assess the effects of four tomato varieties and four planting densities on yield.
Find the one-sided 99% confidence interval for the population mean caffeine content of a cup of coffee that claims "at least...."
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