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School: Harvard
Course: Information Theory
Harvard SEAS ES250 Information Theory Gambling and Data Compression 1 1.1 Gambling Horse Race Denition The wealth relative S (X ) = b(X )o(X ) is the factor by which the gamblers wealth grows if horse X wins the race, where b(X ) is the fraction of the ga
School: Harvard
Course: Information Theory
Harvard SEAS ES250 Information Theory ES250 Project Description Fall 200708 The goal of this project is for you to explore an area of contemporary information theory to complement materials in class. Since information theory is a relatively young and evo
School: Harvard
Course: Information Theory
Course information Information theory overview Some terms and concepts Entropy ES250 Information Theory Besma SMIDA Tuesday/Thursday 12:30pm, Cruft 319 Fall 200809 B. Smida (SEAS) ES250 Fall 200809 1 / 18 Course information Information theory overview S
School: Harvard
Engineering Sciences 50 Laboratory 3 Purpose: These exercises are meant to acquaint you with the characteristivs and typical applications of flipflops. Background: The exercises are divided into two main sections each with several parts. Section on
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 6 Due: April 2, 2015 Exercise 1. Total Probability, Geometric Random Variables, and Expectation Independent trials, resulting in one of the outcome
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 5 Due: March 26, 2015 Exercise 1. Playing Cards Suppose a standard deck of 52 playing cards is thoroughly shued and a single card is drawn. An ace
School: Harvard
Course: Information Theory
Harvard SEAS ES250 Information Theory ES250 Course Information Fall 200809 Hours and location Lectures Problem sessions TTh 12:30pm, Cruft 319 TBA Teaching sta Instructor Besma Smida bsmida@seas.harvard.edu 6174967661 MaxwellDworkin 117 Oce Hours: Wed
School: Harvard
Course: Information Theory
Harvard SEAS ES250 Information Theory ES250 Project Description Fall 200708 The goal of this project is for you to explore an area of contemporary information theory to complement materials in class. Since information theory is a relatively young and evo
School: Harvard
Course: Information Theory
Course information Information theory overview Some terms and concepts Entropy ES250 Information Theory Besma SMIDA Tuesday/Thursday 12:30pm, Cruft 319 Fall 200809 B. Smida (SEAS) ES250 Fall 200809 1 / 18 Course information Information theory overview S
School: Harvard
Course: Information Theory
Harvard SEAS ES250 Information Theory Midterm Exam Solutions 1. (15 points) Let X be the waiting time for the rst heads to appear in successive ips of a fair coin. Thus, for example, Prcfw_X = 3 = ( 1 )3 . 2 (a) (5 points) Find H (X ). (b) (5 points) Find
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 6 Due: April 2, 2015 Exercise 1. Total Probability, Geometric Random Variables, and Expectation Independent trials, resulting in one of the outcome
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 5 Due: March 26, 2015 Exercise 1. Playing Cards Suppose a standard deck of 52 playing cards is thoroughly shued and a single card is drawn. An ace
School: Harvard
TXW XSXEP TXW FSRYW XSXEP ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 4 Due: March 12, 2015 Yues note: Midterm 1 is scheduled on Tuesday March 3 (in class.) It is closedbook, with no electro
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 4 Due: March 12, 2015 Yues note: Midterm 1 is scheduled on Tuesday March 3 (in class.) It is closedbook, with no electronics allowed. However, you
School: Harvard
8SXEP TXW ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Solution 3 Date: February 28, 2015 TXW XSXEP Exercise 1. Probability Models Consider two events A and B dened on a common sample space . (a) Expre
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 3 Due: February 26th, 2015 Exercise 1. Probability Models Consider two events A and B dened on a common sample space . (a) Express each of the foll
School: Harvard
Engineering Sciences 50 Laboratory 3 Purpose: These exercises are meant to acquaint you with the characteristivs and typical applications of flipflops. Background: The exercises are divided into two main sections each with several parts. Section on
School: Harvard
Course: Information Theory
Harvard SEAS ES250 Information Theory Gambling and Data Compression 1 1.1 Gambling Horse Race Denition The wealth relative S (X ) = b(X )o(X ) is the factor by which the gamblers wealth grows if horse X wins the race, where b(X ) is the fraction of the ga
School: Harvard
Course: Information Theory
Harvard SEAS ES250 Information Theory ES250 Project Description Fall 200708 The goal of this project is for you to explore an area of contemporary information theory to complement materials in class. Since information theory is a relatively young and evo
School: Harvard
Course: Information Theory
Course information Information theory overview Some terms and concepts Entropy ES250 Information Theory Besma SMIDA Tuesday/Thursday 12:30pm, Cruft 319 Fall 200809 B. Smida (SEAS) ES250 Fall 200809 1 / 18 Course information Information theory overview S
School: Harvard
Engineering Sciences 50 Laboratory 3 Purpose: These exercises are meant to acquaint you with the characteristivs and typical applications of flipflops. Background: The exercises are divided into two main sections each with several parts. Section on
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 6 Due: April 2, 2015 Exercise 1. Total Probability, Geometric Random Variables, and Expectation Independent trials, resulting in one of the outcome
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 5 Due: March 26, 2015 Exercise 1. Playing Cards Suppose a standard deck of 52 playing cards is thoroughly shued and a single card is drawn. An ace
School: Harvard
TXW XSXEP TXW FSRYW XSXEP ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 4 Due: March 12, 2015 Yues note: Midterm 1 is scheduled on Tuesday March 3 (in class.) It is closedbook, with no electro
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 4 Due: March 12, 2015 Yues note: Midterm 1 is scheduled on Tuesday March 3 (in class.) It is closedbook, with no electronics allowed. However, you
School: Harvard
8SXEP TXW ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Solution 3 Date: February 28, 2015 TXW XSXEP Exercise 1. Probability Models Consider two events A and B dened on a common sample space . (a) Expre
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 3 Due: February 26th, 2015 Exercise 1. Probability Models Consider two events A and B dened on a common sample space . (a) Express each of the foll
School: Harvard
TXW XSXEP TXW FSRYW ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Solution 2 Date: February 25, 2015 TXW XSXEP TXW FSRYW Exercise 1. Conditional Probability and the Total Probability Formula Alice and B
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 2 Due: Feb. 19, 2015 Exercise 1. Conditional and Total Probabilities Alice and Bob play the following game of dice. Each round of the game consists
School: Harvard
TXW XSXEP ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Solution 1 Date: February 18, 2015 TXW XSXEP Exercise 1. TX TX TXW a. A (B C) = (A B) (A C) is true by distributive property of sets. b. A (B C) =
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 1 Due: Feb. 12, 2015 Note: Due to the extended due date, this homework contains more problems (8) than a typical homework might contain (56). Plea
School: Harvard
Course: Information Theory
Harvard SEAS ES250 Information Theory Midterm Exam Solutions 1. (15 points) Let X be the waiting time for the rst heads to appear in successive ips of a fair coin. Thus, for example, Prcfw_X = 3 = ( 1 )3 . 2 (a) (5 points) Find H (X ). (b) (5 points) Find
School: Harvard
Course: Information Theory
Harvard SEAS ES250 Information Theory Gaussian Channel 1 Denitions Denition (Gaussian channel) Discretetime channel with input Xi , noise Zi , and output Yi at time i. This is Yi = Xi + Zi , where the noise Zi is drawn i.i.d. from N (0, N ) and assumed t
School: Harvard
Course: Information Theory
Harvard SEAS ES250 Information Theory Channel Capacity 1 1.1 Preliminaries and Denitions Preliminaries and Examples Communication between A (the sender) and B (the receiver) is succesful when both A and B agree on the content of the message. A communicat
School: Harvard
Course: Information Theory
Harvard SEAS ES250 Information Theory ES250 Course Information Fall 200809 Hours and location Lectures Problem sessions TTh 12:30pm, Cruft 319 TBA Teaching sta Instructor Besma Smida bsmida@seas.harvard.edu 6174967661 MaxwellDworkin 117 Oce Hours: Wed
School: Harvard
Course: Information Theory
Harvard SEAS ES250 Information Theory ES250 Course Information Fall 200809 Hours and location Lectures Problem sessions TTh 12:30pm, Cruft 319 TBA Teaching sta Instructor Besma Smida bsmida@seas.harvard.edu 6174967661 MaxwellDworkin 117 Oce Hours: Wed
School: Harvard
Course: Information Theory
Harvard SEAS ES250 Information Theory ES250 Project Description Fall 200708 The goal of this project is for you to explore an area of contemporary information theory to complement materials in class. Since information theory is a relatively young and evo
School: Harvard
Course: Information Theory
Course information Information theory overview Some terms and concepts Entropy ES250 Information Theory Besma SMIDA Tuesday/Thursday 12:30pm, Cruft 319 Fall 200809 B. Smida (SEAS) ES250 Fall 200809 1 / 18 Course information Information theory overview S
School: Harvard
Course: Information Theory
Harvard SEAS ES250 Information Theory Midterm Exam Solutions 1. (15 points) Let X be the waiting time for the rst heads to appear in successive ips of a fair coin. Thus, for example, Prcfw_X = 3 = ( 1 )3 . 2 (a) (5 points) Find H (X ). (b) (5 points) Find
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 6 Due: April 2, 2015 Exercise 1. Total Probability, Geometric Random Variables, and Expectation Independent trials, resulting in one of the outcome
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 5 Due: March 26, 2015 Exercise 1. Playing Cards Suppose a standard deck of 52 playing cards is thoroughly shued and a single card is drawn. An ace
School: Harvard
TXW XSXEP TXW FSRYW XSXEP ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 4 Due: March 12, 2015 Yues note: Midterm 1 is scheduled on Tuesday March 3 (in class.) It is closedbook, with no electro
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 4 Due: March 12, 2015 Yues note: Midterm 1 is scheduled on Tuesday March 3 (in class.) It is closedbook, with no electronics allowed. However, you
School: Harvard
8SXEP TXW ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Solution 3 Date: February 28, 2015 TXW XSXEP Exercise 1. Probability Models Consider two events A and B dened on a common sample space . (a) Expre
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 3 Due: February 26th, 2015 Exercise 1. Probability Models Consider two events A and B dened on a common sample space . (a) Express each of the foll
School: Harvard
TXW XSXEP TXW FSRYW ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Solution 2 Date: February 25, 2015 TXW XSXEP TXW FSRYW Exercise 1. Conditional Probability and the Total Probability Formula Alice and B
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 2 Due: Feb. 19, 2015 Exercise 1. Conditional and Total Probabilities Alice and Bob play the following game of dice. Each round of the game consists
School: Harvard
TXW XSXEP ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Solution 1 Date: February 18, 2015 TXW XSXEP Exercise 1. TX TX TXW a. A (B C) = (A B) (A C) is true by distributive property of sets. b. A (B C) =
School: Harvard
ES 150: Introduction to Probability with Engineering Applications Spring 2015 Professor: Yue M. Lu Homework 1 Due: Feb. 12, 2015 Note: Due to the extended due date, this homework contains more problems (8) than a typical homework might contain (56). Plea
School: Harvard
Engineering Sciences 50 Laboratory 3 Purpose: These exercises are meant to acquaint you with the characteristivs and typical applications of flipflops. Background: The exercises are divided into two main sections each with several parts. Section on