3. Consider a discrete source with an alphabet A = {a1, a2, ** , a1}. Compute the entropyof the source for the following two cases:1(a) The source is uniformly distributed with p(a,) =÷,vl E (1,2, , L}....(b) For a particular k e (1,2, …· , L},p(ax) = 1 and p(aj) = 0,1 # k.

A discrete source is given with an alphabet: A={a1,a2,...,aL} We have to compute the entropy of the…

Answered: 3. Consider a discrete source with an…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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5. Suppose that a stick of length 1 is broked at a point U uniformly distributed on (0,1). Let L be the length of the longer of the two resulting pieces. 0 (a) Find P (L>). (b) 1 Find the cumulative distribution function of L.
Assume that A, B, and C are subsets of a sample space S with Pr(A) = 0.75, Pr(B) = 0.55, Pr(C) = 0.25. 1. Find Pr(A'), Pr(B'), and Pr(C'). Pr(A') = Pr(B') = %3D Pr(C') = 2. If Pr(A U B) = 0.75., find Pr(A n B). Pr(A n B) = 3. Suppose that we know that B and C are disjoint events. Find Pr[B U C]. Pr[B U C] = 4. Suppose that instead of being disjoint C C B. Find Pr[B U C]. Pr[BU C] =
3. 01:26:35 The following two-way table shows the distribution of daily traffic and weather issues in a certain large city. Suppose a day from this city is selected at random. Let event A = heavy traffic and event B = bad weather. Are events A and B independent? Daily Traffic No, P(A) = P(B|A). Нeavy Traffic Light Traffic Total O No, P(A) + P(A|B). O Yes, P(A) = P(A|B). O Yes, P(A) + P(B|A). Bad Weather 25 30 Good Weather 55 15 75 Total 80 20 100 Weather Conditions
Suppose there are three possible states of nature, and the class-conditional PDFS are the Cauchy distributions 1 p(rw;) = 1 i = 1,2,3. (1) 2 1+ bị Let ai = -2, a2 = 0, az = 2, bị = b2 = 1, b3 = 0.5. Let P(wi) = P(w2) = 0.4, P(w3) = 0.2. (a) Find the decision boundaries and the decision regions for the Bayesian decision (b) Calculate the probability of error for the classification done according to this

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3. Consider a discrete source with an alphabet A = {a1, a2, · , a1}. Compute the entropy of the source for the following two cases: (a) The source is uniformly distributed with p(aj) =÷,vI E (1,2, …· , L}. ... (b) For a particular k E (1,2, -…, L}, p(ax) : = 1 and p(a¡) = 0,1 ± k.