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11

Part of 1975 Miklós Schweitzer

Problems(1)

Miklos Schweitzer 1975_11

Source: Shannon entropy

12/30/2008
Let X1,X2,...,Xn X_1,X_2,...,X_n be (not necessary independent) discrete random variables. Prove that there exist at least n2/2 n^2/2 pairs (i,j) (i,j) such that H(X_i\plus{}X_j) \geq \frac 13 \min_{1 \leq k \leq n} \{ H(X_k) \}, where H(X) H(X) denotes the Shannon entropy of X X. GY. Katona
probability and stats