Copy of Homework-Set-03-Solutions.pdf - ICS 311 Spring 2019 Problem Set 03 ​Topic 05 Solutions(26 pts Copyright(c 2016-18 Daniel D Suthers Nodari

# Copy of Homework-Set-03-Solutions.pdf - ICS 311 Spring 2019...

• Homework Help
• 5

This preview shows page 1 - 2 out of 5 pages.

ICS 311, Spring 2019, Problem Set 03, Topic 05 Solutions (26 pts) Copyright (c) 2016-18 Daniel D. Suthers, Nodari Sitchinava and J. Stelovsky. All rights reserved. These solution notes may only be used ONLY by students in ICS 311 Spring 2019 at the University of Hawaii. #1. Expected Length of Coding Scheme (12 points): 1 for correct solution, 3 for explanation/derivation for each (a), (b), and (c) Suppose that several information sources generate symbols at random from a five-letter alphabet {A, B, C, D, E} with different probabilities. We will try different encoding schemes for encoding these symbols in binary. Given the probabilities and an encoding scheme, you will compute the expected length of the encoding of n letters generated by the information source. You may use any rigorous method of analysis you like, but must show your work and justify your answer. (a) (4 pts) Suppose that the symbols occur with probabilities Pr[A] =0.3, Pr[B] = 0.3, Pr[C] = 0.2, Pr[D] = 0.1, and Pr[E] = 0.1, and the coding scheme encodes these symbols into binary codes as follows: A 001 B 010 C 011 D 100 E 101 What is the expected length of the encoding for these probabilities and encoding? Solution: Let X i be a random variable that defines the size of the encoding of the i -th symbol. Then E[X i ] = 3 * Pr[X i =1] + 3 * Pr[X i =2] + 3 * Pr[X i =3] + 3 * Pr[X i =4] + 3 * Pr[X i =4] = 3 * 0.3 + 3 * 0.3 + 3 * 0.2 + 3 * 0.1 + 3 * 0.1 = 3 And let X be the random variable that defines the size of encoding of n symbols.

#### You've reached the end of your free preview.

Want to read all 5 pages?

• Fall '08
• Barjaktarovic,M

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern