Question: 4. A particle performs a random walk on the vertices of a cube. At each step it remains where it is with probability , or

4. A particle performs a random walk on the vertices of a cube. At each step it remains where it is with probability , or moves to one of its neighbouring vertices each having probability . Let v and w be two diametrically opposite vertices. If the walk starts at v, find: (a) the mean number of steps until its first return to v, (b) the mean number of steps until its first visit to w, (c) the mean number of visits to w before its first return to v

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

A particle performs a random walk on the vertices of a cube. At each step it remains where is with probability 1 /4, or moves to one of its neighbouring vertices each having probability 1/ 4. Let v...

please explain steps 5. Problem. A particle performs a random walk on the integer grid in the plane. It starts at (1,0) and at each step moves one unit up, down, left or right, with probability 1/4...

( a ) A particle performs a random walk on the vertex set of an undirected connected graph G , which for simplicity we assume to have neither loops ( vertices connected to themselves ) nor multiple...

please help me with this Notes: Random Walk A random walk is a stochastic sequence {S,}, with So = 0, defined by Sn = XK. K=1 where { Xx} are independent and identically distributed random variables...

A drunken sailor wanders along main street, which conveniently consists of the Problem 20.3. A drunken sailor wanders along main street, which conveniently consists of the points along the 3: axis...

Create a MineWalker game that lets a user start from the lower-left corner on a grid and attempt to walk to the upper-right corner while avoiding hidden mines. Classes that you will create...

Can you help correct the step() method in the RandomWalk and implement the code to produce the MineWalker GUI? I understand time constraints, however comment stubs for suggestions would be much...

[b] In {one of!) Einstein's seminal work[s], he determined the probability for a Brownian particle to he at a position (x, y) relative to its starting point [0,0]: ?[x.y) = exp [TJxZ + fl] . (2}...

I need help with question 4 It's in Matlab 2. "Random walk" is one of the primary and relatively simple random processes in which the process starts from a neutral position (position = 0) and by...

Methane at 25C is burned in a boiler furnace with 10.0% excess air preheated to 100C, Ninety percent of the methane led is consumed, the product gas contains 10.0mol CO2/mol CO and the combustion...

Management sometimes is described as the art and science of making decisions with too little information. What kinds of additional information would a manager want in the seven examples cited in the...

If taxpyers make all of their incoene from a job and vanoes imentmentr, which division of the IRS would likely imestigate their returns if they were andilod? Wage and Investment Division ( WAD )...

Ajay Singh (audit manager), Janie McKenzie (audit senior), and Jamal Smith (audit staff) are discussing the audit of revenues for Alvarez Enterprises. They are finalizing their plans for substantive...