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).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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!
And please do not copy other's work,very appreciate!!
And please do not copy other's work,very appreciate!!
And please do not copy other's work,very appreciate!!
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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