There are k players, with player i having value vi > 0, i = 1,...,k. In every period, two of the players play a game, while the other k − 2 wait in an ordered line. The loser of a game joins the end of the line, and the winner then plays a new game against the player who is first in line. Whenever i and j play, i wins with probability vi/(vi+vj) (a) Define a Markov chain that is useful in analyzing this model.

(b) How many states does the Markov chain have?

(c) Give the transition probabilities of the chain.

He that is measured at 220° is a reflex angle. the opposite angle is obtuse. find the measure of obtuse .

Max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.

Roger could feed 5 walruses with 4 kilograms of fish. how many walruses could he feed with 7.2 kilograms of fish?