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).

Hi, I need some help foor this question. Please do not copy with chatgpt. Please write clear I need some explain. The chatgpt is not correct. Thanks!  Rick and Morty accidentally created a highly contagious virus that is capable of killing the aliens on planet Zoinks in under a day. So far, only 8% of the population of Zoinks has been infected. Rick and Morty whipped up a test for the virus, but the test is not perfect: 90% of the time it correctly identifies a healthy alien as not having the virus, but 25% of the time it incorrectly identifies an infected alien as virus-free. One of the aliens on the planet is worried that they may have contracted the virus, so they takes 20 independent tests. Of these 20 tests, 6 indicate that they have the disease and the remaining 14 indicate that they do not. With this information, what is the probability that the alien actually has the virus?  Please First use Bayes' formula, then for the conditional probability, and then need to use binomial…

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!

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. and and Very very grateful! And please do not copy other's work!!Thanks!

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!

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. and 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!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, help solve this question with a friendly solution. Please, I need the R Codes as well. Take you very much!

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!

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. and and Very very grateful!