Mathematical methods in communication Lecture 2
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چکیده
Example 2 (Convexity of a probability vector space) Show that the probability vector space is a convex set. Answer: Consider a random variable X with alphabet X = 1, ..., k. The probability vector space PX = [PX (1) , PX (2) , ..., PX (k)] ∈ R, is the set of all vectors for which PX (i) ≥ 0 ∀i ∈ X , and ∑K i=1 PX (i) = 1. Now consider two probability vectors P (1) X and P (2) X , and the vector
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Example 2 (Convexity of a probability vector space) Show that the probability vector space is a convex set. Answer: Consider a random variable X with alphabet X = 1, ..., k. The probability vector space PX = [PX (1) , PX (2) , ..., PX (k)] ∈ R, is the set of all vectors for which PX (i) ≥ 0 ∀i ∈ X , and ∑K i=1 PX (i) = 1. Now consider two probability vectors P (1) X and P (2) X , and the vector
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