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1. Assume X, are independent and identically distributed with P(X₁ = 1) = p, P(X1 = 0) = r and P(X₁ = = Let SnXi, n = 1, 2, .... -1) = q. where p, r,q > 0 and p+r+q = 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(S101|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 = = Let SnXi, n = 1, 2, .... -1) = q. where p, r,q > 0 and p+r+q = 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(S101|S7 = 0). iv. ES and var(Sn).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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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!

 

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And please do not copy other's work,very appreciate!!

And please do not copy other's work,very appreciate!!

1. Assume X, are independent and identically distributed with P(X₁ = 1) = p, P(X1 = 0) = r and P(X₁ = = Let SnXi, n = 1, 2, .... -1) = q. where p, r,q > 0 and p+r+q = 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(S101|S7 = 0). iv. ES and var(Sn).
Transcribed Image Text:1. Assume X, are independent and identically distributed with P(X₁ = 1) = p, P(X1 = 0) = r and P(X₁ = = Let SnXi, n = 1, 2, .... -1) = q. where p, r,q > 0 and p+r+q = 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(S101|S7 = 0). iv. ES and var(Sn).
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