Problem 3 Consider a random walk on the integers. Suppose we start from 0, and at...
Problem 3 Consider a random walk on the integers. Suppose we start from 0, and at each step, we either go left or right with probability 1/2, ie, Xo--0, and Xt+1 Xt+Zt, where Zt-1 with probability 1/2, and Zt1 with probability 1/2. What is the probability distribution of XT? What is E(X) and Var(XT)? Problem 3 Consider a random walk on the integers. Suppose we start from 0, and at each step, we either go left or right with probability...
4. (Dobrow 2.5) Consider a random walk on {0,...,k}, which moves left and right with respective probabilities q and p. If the walk is at 0 it transitions to 1 on the next step. If the walk is at k it transitions to k−1 on the next step. This is called random walk with reflecting boundaries. Assume that k = 3, q = 1/4, p = 3/4, and the initial distribution is uniform. (a) Find the transition matrix. (b) Find...
2. Problem 2.5. Consider a random walk on 10..... which movies left and right with respective probabilities a and p. If the walk is at 0 it transitions to 1 on the next step. If the walk is at k it transitions to k-1 on the next step. This is called random walk with reflecting boundaries. Assume that k 3, =1/4, p = 3/4, and the initial distribution is uniform. For the following, use technology if needed. (a) (10.1.X2 }...
python / visual studio Problem 1: Random Walk A random walk is a stochastic process. A stochastic process is a series of values that are not determined functionally, but probabilistically. The random walk is supposed to describe an inebriated person who, starting from the bar, intends to walk home, but because of intoxication instead randomly takes single steps either forward or backward, left or right. The person has no memory of any steps taken, so theoretically, the person shouldn't move...
python / visual studio Problem 1: Random Walk A random walk is a stochastic process. A stochastic process is a series of values that are not determined functionally, but probabilistically. The random walk is supposed to describe an inebriated person who, starting from the bar, intends to walk home, but because of intoxication instead randomly takes single steps either forward or backward, left or right. The person has no memory of any steps taken, so theoretically, the person shouldn't move...
10 and 11 please LSM 5 Part C. Suppose that you are walking on a straight line. You start at position Xo =0, and only walk in the positive direction. Your positions after taking the ith step is denoted by X,. For each step, your step size, denoted by S, feet. Assume that sizes of different steps are m 8. (10 credits) Let Xy be your position after taking N steps where N is a given = X,-X,-, is a...
LSM 5 Part C. Suppose that you are walking on a straight line. You start at position X, -0, and only walk in the positive direction. Your positions afcer taking the ith step is denoted by X,. For each step, your step size, denoted by S, = X,-X,-ı , is a random variable uniformly distributed between 1 foot and 2 eet. Assume that sizes of different steps are mutually independent. 8. (10 credits) Let Xy be your position after taking...
a random variable Z with non-zero Consider probability on all the positive integers, that is PIZ k Cak,k = 1,2,... ,co, where 0 < a < 1. Note that B* = if |B1. k-0 -8 i) Specify the constant C (this should not be expressed as a summation) so that this is a valid function. Explain. (5 Points) probability mass i Specify a procedure for simulating Z, given only a standard uniform random number gener- ator, i.e. UUniform[0,1]. (10 Points)...
Suppose Alice is sitting at a circular table with 4 chairs labeled {1, 2, 3, 4} and sitting initially at a random chair. Every minute she moves to her left or right at random with equal probability. Consider the Markov chain associated to the sequence of her positions X0, X1, . . . . 1. Write the state space, the distribution of X0 and the distribution of X1. 2. Write the transition matrix. 3. Assume she is at chair one...
LSM 5 Part C. Suppose that you are walking on a straight line. You start at position Xo , and only walk in the positive direction. Your positions after taking the ith step is denoted by X,. For each step, your step size, denoted by S, . X,-X,-ı , is a random variable uniformly distributed between 1 foot and 2 feet. Assume that sizes of different steps are mutually independent 8. (10 credits) Let X, be your position after taking...