Monte carlo method

Q5-Q7. Bivariate analysis choice Q5. Suppose Nike is interested in determining whether gender (M/F) is associated with Nike shoes use types (i.e., no/light/medium/heavy users). Explain which analysis is the most appropriate one among cross-tabulation, ANOVA, and regression analysis. Q6. A researcher is interested in the relationship between purchase amounts at Amazon.com and the age of respondents. Explain which analysis is the most appropriate one among cross-tabulation, ANOVA, ar regression analysis. Q7. A retailer wonders whether purchase amounts are different between male and female customers. Explain which analysis is the most appropriate one among cross-tabulation, ANOVA, and regression analysis.Problem 1 [4 + 4 = 8 points]. 1) Given the following four Markov chains with 2, 3, 4, 5 states respectively, identify if the single recurrent class in each Markov chain is periodic or not. S1 S2 S1 S1 S2 S1 S2 $5 S3 S3 S2 $4 S3 S4 (a) (b) (c) (d) 2) Now assume that you are given a /V-state Markov chain, in which each state has bi-directional connections with its two neighboring states (i.e., the neighboring states of S, are S2 and Sy; the neighboring states of S2 are S, and S3, ..., and the neighboring states of SN_1 are SN-2 and SN). Identify under what conditions (i.e., what values of N) will this N-state Markov chain have a periodic recurrent class, and justify your answer.Mr. Adam is a coffee addict. He keeps switching between three brands of coffee, say A, B, and C, from week to week according to a discrete Markov chain with the following transition probability matrix: 0.2 0.3 0.5 P = 0.1 0 0.9 0.55 0 0.45 1. Check whether the Markov chain is an irreducible chain or not? 2. Is the Markov chain is periodic or aperiodic? 3. Is the Markov chain has a unique stationary distribution? 4. If Mr. Adam is using brand A this week (i.e., week 1), what is the probability distribution of the brand he will be using in week 20?(12 points) (a) Consider a Markov chain with transition matrix 0.3 0.7 0 P = 0 0.2 0.8 0.7 0.1 0.2 Does the limit of this Markov Chain exist? If yes, find the limit. If not, show your explanation