Which statement(s) is/are false about the Chi Square distribution?

A. As the degrees of freedom increases, the Chi Square distribution approaches a normal distribution.

B. The chi-square distribution is always right skewed, regardless of the value of the degrees of freedom parameter.

C. The chi-square statistic is always positive.

D. As the degrees of freedom increases, the shape of the chi-square distribution becomes more skewed.

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) Problem 7.4 (10 points) A Markov chain X0,X1,X2,. . . with state space S = {1,21 3,4} has the following transition graph: (3) Provide the transition matrix for the Markov chain. (b) Determine all recurrent and all transient states. Q.4 [12 marks] Give examples for Markov chains with the following properties. (a) The Markov chain has a state which is both transient and essential. [3 marks] (b) The Markov chain has a state which is null recurrent and aperiodic. [3 marks (c) The Markov chain has a stationary but not a limiting distribution? [3 marks] (d) The Markov chain has a stationary distribution which is not unique. 3 marks]