Suppose the alphabet is [A,B,CI, and the known probability distribution is PA 05, PBE 0.4, Pc 0.1. For simplicity, let's also assume that both encoder and decoder know that the length of the messages is always 3, so there is no need for a terminator. i. How many bits are needed to encode the message BBB by Huffman coding? ii How many bits are needed to encode the message BBB by Arithmetic coding? iii. Which coding method achieves a lower bit rate in this case? Why? Show your work