A source has an alphabet (a, az, a3, a4} with corresponding probabilities (0.1,0.2, 0.3, 0.4). (i) Find the entropy of the source. (ii) Identify what is the minimum required average code word length to represent this source for error-free reconstruction? (iii) Design a Huffman code for the source and compare the average length of the Huffman code with the entropy of the source. (iv) Design a Huffman code for the second extension of the source (take two letters at a time). What is the average code word length? What is the average number of required binary letters per each source output letter? (v) Identify which scheme is more efficient: The Huffman coding of the original source or the Huffman coding of the second extension of the source? Briefly explain your answer to get full credit.