Markov chain

For each of the following transition matrices. determine whether the Markov chain with that transition matrix is regular: (1) is the Markov chain whose transition matrix whose transition matrix Is 0 1 0 0 0.2 0.8 1 0 [J regular? (Yes or No) 5 (2) is the Markovr chain whose transition matrix-whose transition matrix is 0 1 0 [L1 11.4 0.5 0 1 0 regular? (Yes or No) - E (3) Is the Markov chain whose transition matrix whose transition matrix is 1 O 0 0.8 0 0.2 0.8 0.2 0 regular? (Yes or No) (4) is the Markov chain whose transition matrix vmose transition matrix is 0 1 0 08 0 02 O 1 0 regular? (Yes or No) I able 2. Lillietors tests for normality. Dependent variable is "Change in BMI." Factor variable is Sex. Sex = Female Lilliefors (Kolmogorov-Smirnov) normality test data: Change.in.BMI D= 0.073632, p-value =0.7142 Sex = Male Lilliefors (Kolmogorov-Smirnov) normality test data: Change,in.BMI D = 0.04, p-value = 0.9555 Table 3. Levene's tests for homogeneity of variance. Dependent variable is "Change in BMI." Factor variable is Sex. DF F value PC(>F) group 0. 003 0. 9564 98 Refer to Table 2 and Table 3. What single conclusion would you draw from the information in these 2 tables together? You would reject the null hypotheses. Your data meet both statistical assumptions for a t-test. Your data are not normally distributed. The means of your data are different.1. Consider the Markov chain with the following transition matrix. 0 0.5 0.5 0.5 0 0.5 0.5 0.5 0 (a) Draw the transition diagram of the Markov chain. (b) Is the Markov chain ergodic? Give a reason for your answer. (c) Compute the two step transition matrix of the Markov chain. (d) What is the state distribution *, for t = 2 if the initial state distribution for t = 0 is no = (0.1, 0.5, 0.4) T?Bivariate Distributions What is the bivariate probability density function (pdf) and its properties? Marginal, joint, and conditional distributions Expected values and variance calculation in bivariate distributions Marginal, joint, and conditional expectations Covariance