Question 3: AEP [25 marks total] **All students are expected to attempt this question. Let X be an ensemble with outcomes x = {h, t} with pk = 0.8 and p, = 0.2. Consider XN - e.g., N i.i.d ips of a bent coin. a) Calculate H (X). [3 Marks] b) What is the size of the alphabet XN of the extended ensemble X N ? [3 Marks] c) What is the Raw bit content H0(X4)? [4 Marks] d) Express Entropy H (X N ) as a function of N. [5 Marks] e) Let 85 be the smallest set of N outcome sequences with P(x 6 85) 2 1 6 where 0 S (5 S 1. Use any program language of your choice to plot HXN) ('Normalised Essential Bit Content') vs 6 for various values of N (include some small values of N such as 10 as well as large values greater than 1000. Describe your observations and comment on any insights. [10 Marks]