3. Consider an i.i.d. sequence X1, ... , Xn, with all random variables being Bernoulli with P(X = 1) = p and P(X = 0) =

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3 Consider An I I D Sequence X1 Xn With All Random Variables Being Bernoulli With P X 1 P And P X 0 1 (29.4 KiB) Viewed 32 times

3. Consider an i.i.d. sequence X1, ... , Xn, with all random variables being Bernoulli with P(X = 1) = p and P(X = 0) = 1-p (akin to the lottery problem discussed in class). The e-typical set of length-N is defined as T{) = {x\ \\ 1032 P(21.In) log2 - H(X) )} (1) If a(x) is the fraction of ones in any sequence x (number of ones divided by N), show that VxETEM), E P- 1-P log2 р <a (x) < p + 1-p log2 р