Consider the random walk from HW3 Task 1 with a boundary of [-3, 3] depicted below. What is the transition probability x? Enter the answers to two decimal places.

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Chapter1: Combinatorial Analysis
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**Random Walk Transition Probability**

Consider the random walk from HW3 Task 1 with a boundary of \([-3, 3]\) depicted below. What is the transition probability \(x\)? Enter the answers to two decimal places.

**Diagram Explanation:**

The diagram shows a series of states represented by circles labeled from \(-3\) to \(3\). Arrows between these states and looping arrows around states depict possible transitions and their corresponding probabilities:

- States: \(-3, -2, -1, 0, 1, 2, 3\).
- Transition probabilities \(x\) exist between adjacent states, allowing movement to the left or right.
- Looping arrows at each state represent the probability of remaining in the current state, labeled as \(y\) for central states (\(-2\) to \(2\)) and \(z\) for boundary states (\(-3, 3\)).
- The diagram suggests symmetrical transitions outward from the center.

**Text box for answer:**

- Input: The specific value for \(x\) is suggested as **0.5**.
Transcribed Image Text:**Random Walk Transition Probability** Consider the random walk from HW3 Task 1 with a boundary of \([-3, 3]\) depicted below. What is the transition probability \(x\)? Enter the answers to two decimal places. **Diagram Explanation:** The diagram shows a series of states represented by circles labeled from \(-3\) to \(3\). Arrows between these states and looping arrows around states depict possible transitions and their corresponding probabilities: - States: \(-3, -2, -1, 0, 1, 2, 3\). - Transition probabilities \(x\) exist between adjacent states, allowing movement to the left or right. - Looping arrows at each state represent the probability of remaining in the current state, labeled as \(y\) for central states (\(-2\) to \(2\)) and \(z\) for boundary states (\(-3, 3\)). - The diagram suggests symmetrical transitions outward from the center. **Text box for answer:** - Input: The specific value for \(x\) is suggested as **0.5**.
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