Alice is designing a miniature light sensor which will transmit measurements to her PC. The sensor can record one of six values S = {a,b,c,d,e,f}, with probability distribution p=[1/4, 1/8, 1/8, 1/4, 1/8, 1/8]. (i) Calculate the entropy of the source (ii) Having found the entropy of the source, and recalling that entropy refers to the "uncertainty" of a symbol showing up, calculate the uncertainty that the symbol that shows up is either in the set {a,b} or not. (iii) Find the prefix free code for this source using Shannon-Fano coding, calculate its average wordlength and discuss its relationship with the entropy (iv) Find two different optimal binary codes for this source using Huffman coding, calculate their average wordlengths and discuss their relationship with the entropy. (v) Alice wishes to explore all the possible prefix-free binary codes that can be used to encode the six values, using words of no more than 3 bits. Make a list of all the sets of parameters n, n2, n3 (i.e. numbers of words of lengths 1, 2, and 3 respectively) for which a suitable code exists. Discuss the relationship of this result with your findings in (iii) and (iv). Alice is designing a miniature light sensor which will transmit measurements to her PC. The sensor can record one of six values S = {a,b,c,d,e,f}, with probability distribution p=[1/4, 1/8, 1/8, 1/4, 1/8, 1/8]. (i) Calculate the entropy of the source (ii) Having found the entropy of the source, and recalling that entropy refers to the "uncertainty" of a symbol showing up, calculate the uncertainty that the symbol that shows up is either in the set {a,b} or not. (iii) Find the prefix free code for this source using Shannon-Fano coding, calculate its average wordlength and discuss its relationship with the entropy (iv) Find two different optimal binary codes for this source using Huffman coding, calculate their average wordlengths and discuss their relationship with the entropy. (v) Alice wishes to explore all the possible prefix-free binary codes that can be used to encode the six values, using words of no more than 3 bits. Make a list of all the sets of parameters n, n2, n3 (i.e. numbers of words of lengths 1, 2, and 3 respectively) for which a suitable code exists. Discuss the relationship of this result with your findings in (iii) and (iv).