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

See similar textbooks