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Q1: Consider the output of a digital source that generates 4-bit binary words. Let N be the number of 1's in a generated word. Also, let X = 1 if the majority of the bits is 1, and let X = 0 otherwise. Finally, let Y = 1 if the number of 1's is even, and let Y = 0 otherwise. (a) Draw diagrams clearly illustrating the functional mapping for each of these three rvs. (b) Evaluate Pr[N > 1|X = 1], Pr[N > 1|X = 1,Y = 1] and Pr[X = Y]. (c) Draw the prof and the cdf of each of these rvs. These are the marginal distri- butions