Mathematical Methods in Communication Lecturer: Haim Permuter Scribe: Morag Agmon and Tirza Routtenberg
نویسندگان
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
منابع مشابه
Mathematical methods in communication Lecture 2 Lecturer : Haim
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
متن کاملMathematical methods in communication Lecture 2
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
متن کاملAppendix A : Introduction to Probability and stochastic processes
Lecturer: Haim Permuter Scribe: Shai Shapira and Uri Livnat " The probability of an event is the ratio of the number of cases favorable to it, to the number of all cases possible when nothing leads us to expect that any one of these cases should occur more than any other, which renders them, for us, equally possible. " Probability space formalizes three interrelated ideas by three mathematical ...
متن کاملMathematical methods in communication Lecture 7
I. DIFFERENTIAL ENTROPY AND THE GAUSSIAN CHANNEL A. Differential Entropy Let X be a random variable with a continuous alphabet. • FX(x) = Pr(X ≤ x) Cumulative Distribution Function {CDF}. F (x) is a short notation for FX(x). • fX(x) = dFX(x) dx Probability Density Function {PDF} (in this course we will assume that the derivative exists). f(x) is a short notation for fX(x). Definition 1 ( Differ...
متن کاملMulti - user information theory 2 Lecture 6
The broadcast channel is a communication channel in which there is one sender and several receivers, as presented in Fig. 1. The broadcast channel (BC) was first introduced by Cover [4].
متن کامل