1. Assume X, are independent and identically distributed with P(X₁ = 1) = p, P(X₁ = 0) = r and P(X₁ = −1) = q. where p, r,q> 0 and p+r+ q = 1. Let Sn = Σ²²±1 Xi, n = 1, 2, … … …. i=1 (a) Prove that {S1, S2,…..} is an irreducible Markov chain with state space S = {0, 1, 2,...} and write down its transition matrix. (b) Is the chain aperiodic? (c) Find expressions for: i. P(S3 = 2). ii. P(S₁ = 1|S₁ = 1). iii. P(S10=1|S7 = 0). iv. ES and var(Sn).
1. Assume X, are independent and identically distributed with P(X₁ = 1) = p, P(X₁ = 0) = r and P(X₁ = −1) = q. where p, r,q> 0 and p+r+ q = 1. Let Sn = Σ²²±1 Xi, n = 1, 2, … … …. i=1 (a) Prove that {S1, S2,…..} is an irreducible Markov chain with state space S = {0, 1, 2,...} and write down its transition matrix. (b) Is the chain aperiodic? (c) Find expressions for: i. P(S3 = 2). ii. P(S₁ = 1|S₁ = 1). iii. P(S10=1|S7 = 0). iv. ES and var(Sn).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
Related questions
Question
Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.
Very very grateful!
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 57 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning