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Question 12 10 pts Setup A gambler plays a game where a coin is flipped. If the result comes up "head" the pambler wirs 1 dollar, and at the result comes up til" the cambler loses 1 dollar Assume that the coin is fair --- ichas 1/2 chance of showing head' and 1/2 chance of showing tail The vambler starts with $2. The gambler will continue to play the game until the amount of money (that the samler has reaches 54. or the gambler has no more money to play, camely the amount of money reaches $0 When either scenario happens, the gambler stop playing Parta) Question: The amount of money that this gambler hos forms Marko chain. The posible states are $0, 51, 52, 53, 54 Write down the transition to Instruction Index the mark in the order of 50, 51, 52.53.54 Instruction Just write down the answer no need to justify or pain Part Question: Recall that the cambler initially has 52 Write down the probability in tribution of the amount of money the cameras after the two Instruction Show all the required steps and explain the steps. This question will be onded based on the intermediate steps and their explanations, and of Just bed on the fall answer Part Question: Fied two stationary distributions of this Markovci Instruction You can either postulate stationary distributions, and verify that they satisfy the definition of stationary distributions or solve systems of lines equations to find the stationary distributions Instruction This question will be graded based on the validity of your drivation and not liat based on the final answer ha Question 12 10 pts Setup A gambler plays a game where a coin is flipped. If the result comes up "head" the pambler wirs 1 dollar, and at the result comes up til" the cambler loses 1 dollar Assume that the coin is fair --- ichas 1/2 chance of showing head' and 1/2 chance of showing tail The vambler starts with $2. The gambler will continue to play the game until the amount of money (that the samler has reaches 54. or the gambler has no more money to play, camely the amount of money reaches $0 When either scenario happens, the gambler stop playing Parta) Question: The amount of money that this gambler hos forms Marko chain. The posible states are $0, 51, 52, 53, 54 Write down the transition to Instruction Index the mark in the order of 50, 51, 52.53.54 Instruction Just write down the answer no need to justify or pain Part Question: Recall that the cambler initially has 52 Write down the probability in tribution of the amount of money the cameras after the two Instruction Show all the required steps and explain the steps. This question will be onded based on the intermediate steps and their explanations, and of Just bed on the fall answer Part Question: Fied two stationary distributions of this Markovci Instruction You can either postulate stationary distributions, and verify that they satisfy the definition of stationary distributions or solve systems of lines equations to find the stationary distributions Instruction This question will be graded based on the validity of your drivation and not liat based on the final answer ha

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