A random variable X has an alphabet that given by X={a,b,c,d,e, f}, and has a probability distribution Px = {0.40, 0.25, 0, 15, 0.10, 0.06, 0.04}. 1. Determine a Huffman code for the alphabet. 2. Compute the entropy H(X). 3. Determine the expected value for the length of a code word and compare with the entropy. 4. Determine the expected values of the number of ZEROS and the number of ONES in an ar- bitrary length and an arbitrary distribution of code words. 5. A binary asymmetric channel will be employed to transmit the information. The probability of a bit-flip in transmitting a ZERO is p, while the probability of a bit-flit in transmitting a ONE is q where p+q = 1. If X is the input to the chan- nel and Y is output, plot the mutual information between X and Y as a function of p. 6. Determine the value of the channel property, p that maximizes the mutual information.