Poirot said:
(1)Consider the expected duration of the modified random walk. Show that conditioning on the first step produces a recurrence equation of the following form.Ea = ˜pEa+1 + ˜qEa−1 + ˜c.
(2)Clearly identify the values of ˜p, ˜q and ˜c in terms of p, q and r.
Thanks
A modified random walk is a mathematical model that describes the movement of a particle or agent in a random manner. It differs from a traditional random walk by incorporating additional factors such as directionality or underlying patterns.
The expected duration of a modified random walk can be calculated by taking the average of all possible durations of the walk. This can be done by multiplying the probability of each step by the number of steps and then summing all of these values.
The recurrence equation in modified random walk analysis is a mathematical equation that calculates the probability of a particle or agent returning to its starting position after a certain number of steps. It takes into account the directionality and underlying patterns in the movement.
Modified random walk analysis can be applied in various fields such as finance, biology, and physics. It can be used to model the movement of stock prices, the spread of diseases, or the diffusion of particles in a solution. It can also be used to optimize search algorithms or simulate animal foraging behavior.
Modified random walk analysis is based on mathematical models and may not accurately reflect real-world scenarios. It also assumes that the movement is completely random, which may not always be the case. Additionally, the results of modified random walk analysis may be sensitive to the initial conditions and parameters used in the model.