Note. Read the given questions very carefully. Please choose the missing values indicated in the following problems. Answer copies having the same Markov matrix will not be considered for marking. The total time allowed to solve the first part of the question paper and uploading a single pdf file of answers is 1 hour and 15 minutes. The second part of the paper will start at 7:30 pm and ends at 8:45 pm. No extra time and resubmission will be allowed. Use your time carefully. Good luck.

Q.1 Given the following Markov matrix. Answer the questions listed below.

(1.1 Given the following Markov matrix. Answer the questions listed below. (16 ma rks) 0 0.4 0 P: 0.2 0 0 0 0 0 0 0 0 0.2 a. Fill the empty places with non-zero values in the above matrix P and verify whether it is a transition matrix or not? b. Write any two Cha pman-Kolmogorov equations of your choice. Apply any one equation to the given transition matrix P. c. Check whether the Markov chain of matrix P is reducible or not? d. Sketch a transition diagram of matrix P. e. What will be the stable distribution matrix? f. Classify the chain by identifying transient, recurrent, and absorbing states. g. Check whether it is possible to verify a non-null recurrent state? h. Find the period of recurrent states, if exist