Many texts draw figure 81 in the form of a venn diagram, Ask an Expert

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Many texts draw figure 8.1 in the form of a Venn diagram (figure 8.2). Discuss why this diagram is a misleading representation of entropies. Hint: consider the three-variable ensemble XY Z in which x ∈ {0, 1} and y ∈ {0, 1} are independent binary variables and z ∈ {0, 1} is defined to be z = x + y mod 2

Figure 8.2.

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