Consider a random walk on {0, 1, . . . , N } with jump probabilities p(x,x+1)=1/3, p(x,x−1)=2/3 for1≤x≤N−1 p(0,0)=1−c, p(0,1)=c, p(N,N)=1−c, p(N,N−1)=c with p(x, y) = 0 for all other cases. (Here c is a fixed number in (0, 1).) Find the expected return time to 0 if we start the process there.
please answer it asap due in 10 hours. thanks
Consider a random walk on {0, 1, . . . , N } with jump probabilities...
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...
Consider a random variable X, that takes values 0 and 1 with probabilities P(0) = P(1) = 0.5. Then, X = 0 with probability 0.5 and X = 1 with probability 0.5. What is the expected value of X? 0 0.25 0.5 1
1. Random Walk: Consider a random walk described by the following probability rules: P(+x) 0.5; P(-x) 0.1; P(ty) 0.2; P(-y) 0.2 (a) Is the walk biased? If so in which direction? Explain. (b) Compute the following for N steps if the step size is equal to a: <x>, <y>, <x>, <y (c) After long time (after large number of steps, where would the object be found? (find σ, and
1. Random Walk: Consider a random walk described by the following...
1-D Random Walk: Consider a random walk described by the following probability rules: P(+x) = 0.5; P(-x) = 0.1 ; P(ty) = 0.2; P(-y) = 0.2 (a) Is the walk biased? If so in which direction? Explain. (b) Compute the following for N steps if the step size is equal to a: <x, y>, <x>, <y'> (c) After long time (after large number of steps, where would the object be found? (find Ox, Ox I.
1-D Random Walk: Consider a...
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...
(1 point) If X is a binomial random variable, compute the probabilities for each of the following cases: (a) P(X < 3), n = 9, p = 0.3 Probability = (b) P(X > 4), n = 5, p = 0.3 Probability = (c) P(X<5), n = 7.p = 0.35 Probability = (d) P(X > 6), n = 7, p = 0.3 Probability =
(1 point) If X is a binomial random variable, compute the probabilities for each of the following cases: (a) P(X < 1), n = 4, p = 0.1 Probability = (b) P(X > 1), n = 6, p = 0.1 Probability = (c) P(X < 3), n = 6, p = 0.3 Probability = (d) P(X > 2), n = 3, p = 0.4 Probability =
Problem 1 (15%): Find the following probabilities for two normal random variables Z = N(0,1) and X = N(-1,9). (a) P(Z > -1.48). (b) P(|X< 2.30) (c) What is the type and the parameters of the random variable Y = 3X +5?
(1 point) If X is a binomial random variable, compute the probabilities for each of the following cases: (a) P(X < 1), n = 7, p = 0.3 Probability = (b) P(X > 5), n = 7, p = 0.1 Probability = (C) P(X < 6), n = 8, p = 0.5 Probability = (d) P(X > 2), n = 3, p = 0.5 Probability =
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...