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A particle executes a simple unrestricted random walk on the line: a step to the right...
A particle executes a simple unrestricted random walk on the line: a step to the right...
A particle executes a simple unrestricted random walk on the line: a step to the right of length 1 occurs with probability 0.56 and a step to the let of length 1 occurs with probability 0.44. Initially the particle is at the onigin. Select the option that gives an approximate value for the probability that the particle will be less than 6 units from the origin after 100 steps, calculated using an appropriate continuity correction. Select one: 0.195 0.238 0.280...
A particle executes a simple unrestricted random walk on the line: a step to the right...
A particle executes a simple unrestricted random walk on the line: a step to the right of length 1 occurs with probability 0 56 and a step to the left of length l occurs with probability 0 44 Initially the particle is at the origin. Select the option that gives an approximate value for the probability that the particle will be less than 6 units from the origin after 100 steps, calculated using an appropriate continuity correction Select one: 0.195...
A particle executes a simple unrestricted random walk on the line: a step to the right...
A particle executes a simple unrestricted random walk on the line: a step to the right of length 1 occurs with probability 0.66 and a step to the left of length 1 occurs with probability 0.34. Initially the particle is at the origin. Calculate the probability that the particle will ever return to the origin.
A particle executes a simple unrestricted random walk on the line: a step to the right...
A particle executes a simple unrestricted random walk on the line: a step to the right of length 1 occurs with probability 0.66 and a step to the left of length 1 occurs with probability 0.34. Initially the particle is at the origin. Calculate the probability that the particle will ever return to the origin.
b) A particle executes an unrestricted random walk on the line starting at the origin. The...
b) A particle executes an unrestricted random walk on the line starting at the origin. The ith step, Zi, has the following distribution: (i) Find the mean and variance of Z,, and hence find the mean and [41 15 12] variance of X the position of the particle after n steps (ii) Find the probability distribution of X, and state the range of X Explain all the steps in your derivation of the distribution (iii) Calculate the following probabilities in...
Topic 3 (About CLT and Bayes'Theorem: 10 marks] A particle moves along the line in a random walk....
Topic 3 (About CLT and Bayes'Theorem: 10 marks] A particle moves along the line in a random walk. That is, the particle starts at the origin (position 0) and moves either 2 units to the right or I unit to the left in independent steps. If the particle moves to the right with probability 2/3, its movement at the ih step is a random variable X, with distribution P(x+2)-2/3 P(X,-)=13 The position of the particle after 400 steps is the...
A particle executes a simple unrestricted random walk on the line: a step to the right of length 1 occurs with probability 0.56 and a step to the let of length 1 occurs with probability 0.44. Initially the particle is at the onigin. Select the option that gives an approximate value for the probability that the particle will be less than 6 units from the origin after 100 steps, calculated using an appropriate continuity correction. Select one: 0.195 0.238 0.280...
A particle executes a simple unrestricted random walk on the line: a step to the right of length 1 occurs with probability 0 56 and a step to the left of length l occurs with probability 0 44 Initially the particle is at the origin. Select the option that gives an approximate value for the probability that the particle will be less than 6 units from the origin after 100 steps, calculated using an appropriate continuity correction Select one: 0.195...
b) A particle executes an unrestricted random walk on the line starting at the origin. The ith step, Zi, has the following distribution: (i) Find the mean and variance of Z,, and hence find the mean and [41 15 12] variance of X the position of the particle after n steps (ii) Find the probability distribution of X, and state the range of X Explain all the steps in your derivation of the distribution (iii) Calculate the following probabilities in...
Topic 3 (About CLT and Bayes'Theorem: 10 marks] A particle moves along the line in a random walk. That is, the particle starts at the origin (position 0) and moves either 2 units to the right or I unit to the left in independent steps. If the particle moves to the right with probability 2/3, its movement at the ih step is a random variable X, with distribution P(x+2)-2/3 P(X,-)=13 The position of the particle after 400 steps is the...
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