Make a Markov chain model of a poker game where the states are the number of dollars a player has. With probability .3 a player wins 1 dollar in a period, with probability .4 a player loses 1 dollar, and with probability . 3 a player stays the same. The game ends if the player loses all his or her money or if the player has 6 dollars (when the game ends, the Markov chain stays in its current state forever). The Markov chain should have seven states, corresponding to the seven different amounts of n1oney: 0, I , 2, 3, 4, 5, or 6 dollars. If you now have $2, what is your probability distribution in the next round? In the round after that?

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24