Question: Consider a walker who walks on a real line starting at 0 with moving one step forward with probability p and backward with probability q,

Consider a walker who walks on a real line starting at 0 with moving one step forward with probability p and backward with probability q, pq+=1. Let Xn describe the position of the walker after n steps.

a. What is the probability that walker is at the point 0 on the line after two steps?

b. What is the probability that walker is at the point −1 on the line after three steps?

c. What is the probability that walker is at the point 3 on the line after three steps?

d. Suppose the walker is at point 4 after 10 steps, does the probability that it will be at point 8 after 16 steps (6 more steps) depend on how it moves to point 4 within the first 10 steps?

e. Are X10−X4 and X16−X12 independent?

f. Are X10−X4 and X12−X8 independent?

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 Probability Statistics Questions!

The choice of a CEO signals potential actions to stakeholders about a firms potential actions. Howard Schultz served as Starbucks CEO for many years; the firm achieved multiple successes during his...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

nodes, but at least its bias can be quantified by Markov Chain L. INTRODUCTION analysis and thus can be corrected via appropriate re-weighting The popularity of online social networks (OSNs) in...

Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...

incorrect document, we'll assume that the homework assignment was not actually completed. Background DBVac is considering adding an additional product to their lineup. The company's Research and...

Through the use of strategic alternatives, companies may compete in a marketplace, achieve its vision, or if no vision has been articulated, decide where it might go and what it might achieve....

Please help to answer the Case study Questions. These Q's are based on Part 1 of this case study project, as well as the Introduction and Business Description in the case study. Read the Introduction...

Due to the changing environment and external triggers, contingency planning is necessary. What qualities make a future issue a ?trigger?? Consider you are on the strategic planning team for a soft...

Create a balanced scorecard to determine which of the companys four product managers should lead the project. (30 points) The scorecard should compare the four possible options across six criteria:...

What approach should Hirsch take with Metropolis? Why? Create a list of 5 risks with the approach you recommend for Hirsch? Take your top 2 risks and discuss how Hirsch could best mitigate each of...

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...

Suppose you purchased, a 18-year, 9.25 percent coupon (annual payments) bond at par. You hold it for 10 years and sell it so that you can take a vacation to British Virgin Islands. At the time you...

For a system is given as figure below with T-2s and T G(s) G(z)= K(+0.8) (z 1)(z 0.6) (i) Determine the range of K for stability using Routh-Hurwitz criterion. (ii) Determine the range of K for...

What is the 20X4 depreciation expense for the scanner? DeltaTech uses the straight-line method. Assets purchased between the 1st and 15th of the month are depreciated for the entire month; assets...

a. Financial statements should aid the user of the statements in making decisions. In your opinion, would the user of the statements be aided if there were a distinction between financial reporting...