Only do B and C please, I already solved for part A

A Markov source with three symbols A = {21, 22, 23} has the following prob- ability distributions p(a) = 1/2, p(22) = 1/3, p(a3) = 1/6, } if i = j P{a/a;} = otherwise (a) Calculate the 1st order entropy, 2nd order entropy, 1 st order conditional entropy, and the entropy rate of this source: (b) Design the 1st order, 2nd order, and 1st order conditional Huffman codes for this source. Calculate the resulting bit rate for each case. Compare it to the corresponding lower and upper bounds defined by the entropy. (c) What is the minim al bit rate achievable with this source? How could you achieve the minimal rate? A Markov source with three symbols A = {21, 22, 23} has the following prob- ability distributions p(a) = 1/2, p(22) = 1/3, p(a3) = 1/6, } if i = j P{a/a;} = otherwise (a) Calculate the 1st order entropy, 2nd order entropy, 1 st order conditional entropy, and the entropy rate of this source: (b) Design the 1st order, 2nd order, and 1st order conditional Huffman codes for this source. Calculate the resulting bit rate for each case. Compare it to the corresponding lower and upper bounds defined by the entropy. (c) What is the minim al bit rate achievable with this source? How could you achieve the minimal rate