Question

In: Statistics and Probability

Q2. Consider a game of tennis from deuce onward. Starting at the state of deuce, if...

Q2. Consider a game of tennis from deuce onward. Starting at the state of deuce, if the server wins, the score is ad-in. If the server then loses the next point, the game is back to deuce. However, if the server wins two points in a row, he wins the game. Similarly, starting at the state of deuce, if the returner wins, the score is ad-out. If the returner then loses the next point, the game is back to deuce. But if the returner wins two points in a row, he wins the game.

Let the probability of winning the point be 0.4. Moreover, the winner gets $10, and the loser pays $10.

Is this game recursive?

Draw and properly label the game tree. If there is a state that recurs, do not go beyond that state.

What is the probability of winning the game in the state of deuce?

What is the probability of winning the game for the server given that he wins the first point after deuce?

What is the value of the game at the state of deuce?

Expert Solution

Answer:

Given that:

Consider a game of tennis from deuce onward. Starting at the state of deuce, if the server wins, the score is ad-in. If the server then loses the next point, the game is back to deuce

Let the probability of winning the point be 0.4. Moreover, the winner gets $10, and the loser pays $10.

Is this game recursive?

Yes, this game is recursive because in a state of non zero payoff , play immediately moves to an absorbing state where each player has only one action available which actions give a particular non zero payoff in further stage .

Draw and properly label the game tree. If there is a state that recurs, do not go beyond that state.

What is the probability of winning the game in the state of deuce?

The probability of winning the game at deuce is 0.2

What is the probability of winning the game for the server given that he wins the first point after deuce?

The probability of winning the game after one point is =0.2*0.2

The probability of winning the game after one point is = 0.04

What is the value of the game at the state of deuce?

The value of game at deuce is equal payoff of 0 as both the players have 0 points at the starting of the game

orchestra answered 1 year ago

3.17 You and I play a tennis match. It is deuce, which means if you win...

3.17 You and I play a tennis match. It is deuce, which means if you win the next two rallies, you win the game; if I win both rallies, I win the game; if we each win one rally, it is deuce again. Suppose the outcome of a rally is independent of other rallies, and you win a rally with probability p. Let W be the event “you win the game,” G “the game ends after the next two rallies,”...

Q2. (25 points) Consider an economy in the United States, starting from the long-run equilibrium denoted...

Q2. (25 points) Consider an economy in the United States, starting from the long-run equilibrium denoted as the point A. Use an aggregate demand and aggregate supply (AD-AS) diagram to show that the economy is in the long-run equilibrium. (Please label variables clearly) a. If the U.S. currency becomes stronger (the value of a dollar increases), there is a change in international variables. How does this situation affect the AD-AS diagram? What will happen to the equilibrium price level and...

A state is starting a lottery game. To enter this lottery, a player uses a machine...

A state is starting a lottery game. To enter this lottery, a player uses a machine that randomly selects six distinct numbers from among the first 30 positive integers. The lottery randomly selects six distinct numbers from the same 30 positive integers. A winning entry must match the same set of six numbers that the lottery selected. The entry fee is 1, each winning entry receives a prize amount of 500,000, and all other entries receive no prize. Calculate the...

Design a text-based game. The game should involve starting from some point in the universe and...

Design a text-based game. The game should involve starting from some point in the universe and seeking or exploring. For example, you could start at the mouth of a cave and seek gold in the halls and caverns. Write out the logic in English and/or pseudocode. Write several lines of JavaScript code that will start the game going, containing control flow statement(s).

Q2: A particle is moving in a constant force field starting at rest from some point...

Q2: A particle is moving in a constant force field starting at rest from some point (x1, x1’) to some higher point (x2, x2’). The potential energy is mgx, where g is the acceleration imparted by the force. Find the path that allows the particle to accomplish the transit in the least possible time.

Q2. Consider a Bertrand game with differentiated products in which two firms simul- taneously choose prices....

Q2. Consider a Bertrand game with differentiated products in which two firms simul- taneously choose prices. The marginal cost for each firm is zero and there are no fixed costs. The demand functions for each firm are: Q1 = 80 − 2P1 + 2P2, Q2 = 80 − 2P2 + 2P1. where P1 is the price set by firm 1, P2 is the price set by firm 2, Q1 is the quantity demanded of firm 1’s product and Q2 is...

Using the Bohr Model of the atom, consider an electron starting in the n=5 state of...

Using the Bohr Model of the atom, consider an electron starting in the n=5 state of a hydrogen atom that emits a photon in the UV range as it drops to lower energy. A) Determine the final state, nf, after the atom emits the photon. B)Calculate the change in energy of the electron. C)Calculate the frequency of the photon emitted. D) Calculate the wavelenght of the photon in nm. Need some help! Thank you in advanced!

Consider the Tragedy of the Commons game from the chapter with two shepherds, A and B,...

Consider the Tragedy of the Commons game from the chapter with two shepherds, A and B, where sA and sB denote the number of sheep each grazes on the common pasture. Assume that the benefit per sheep (in terms of mutton and wool) equals 500-sA-sB implying that the total benefit from a flock of sA sheep is sA(500-sA-sB) and that the marginal benefit of an additional sheep (which is defined by the first partial derivative with respect to sA of...

Consider the following game. There are 10 political positions, 1, · · · , 10, from...

Consider the following game. There are 10 political positions, 1, · · · , 10, from the most liberal to the most conservatives. Two politicians simultaneously choose what position they pick in order to maximize the percentage of votes they can get. 10% of voters are at each position. Voters will vote for the politician they are closer to. If two politicians choose the same position then they each get 50% of the votes. (a) Solve this game by iterative...

A man is playing tennis game. He hits a stationary ball of mass 50 g with...

A man is playing tennis game. He hits a stationary ball of mass 50 g with his racquet. Interpret the energy conversions taking place when he hits ball with racquet. The average force acting on it is 600 N, so that the ball moves with a velocity of 60 m/s .Can you predict the time of hit of the ball when it leaves the racquet using given data? How can you find the change in kinetic energy of moving ball?...