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).

MATLAB: An Introduction with Applications
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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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