Problem 3:a-Let X be a geometrically distributed random variable, i.e.,P(X = k) = p(1 – p*-1,k = 1, 2, 3, ...1. Find the entropy of X.2. Given that X > K, where K is a positive integer, what is the entropy of X?b-The output of a DMS consists of the possible letters x1, x2,..., Xn, which occur withprobabilities p1, P2, , Pn, respectively. Prove that the entropy H(X) of the source is atmost log n. Find the probability density function for which H(X) = logn.

a. Given, Pk = P(X=k) = p(1-p)k-1 , k = 1,2,3... Entropy is given by, H(X) =-∑k=1∞Pk…

a- Let X be a geometrically distributed random variable, i.e., P(X = k) = p(1 – p-', k = 1, 2, 3,... 1. Find the entropy of X. 2. Given that X > K, where K is a positive integer, what is the entropy of X?

a- Let X be a geometrically distributed random variable, i.e., P(X = k) = p(1 – p-', k = 1, 2, 3,... 1. Find the entropy of X. 2. Given that X > K, where K is a positive integer, what is the entropy of X?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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