Asource has an alphabet {a1 , a1, a3, a4} with corresponding probabilities {0.1, 0.2, 0.3, 0.4}. 1. find the entropy of the source. 2. what is the minimum required average code word length to represent this source for error-free reconstruction? 3. design a huffman code for the source and compare the average length of the huffman code with the entropy of the source. 4. 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? 5. which is a more efficient coding scheme: the huffman coding of the original source or the huffman coding of the second extension of the source?