## Introduction to Data Communication Networks

###### Fundamentals of Probability Theory

Introduction

10/12/13

Running Time: 2:43

Fundamentals of probability theory introduction for an undergraduate course in digital communications

Events

10/13/13

Running Time: 27:59

Explores basic quantities related to events: sample space, event probability, Bayes' Theorem, Total Probability Theorem, Mutually Exclusive events, Independent Events, Bernoulli Trials, etc.

Conditional Probability Example

10/14/13

Running Time: 3:13

This problem demonstrates conditional probabilities through a simple computational example. The probability of drawing two specific cards from a deck of cards without replacement is computed.

Binary Symmetric Channel

10/16/13

Running Time: 6:31

This example defines and investigates a communication channel called the binary symmetric channel (BSC).

Repeat Coding

10/17/13

Running Time: 12:19

This example investigates repeat coding, an error control coding scheme that improves transmission reliability at the expense of reduced data rates.

CDFs and PDFs

10/22/13

Running Time: 11:06

Gives an overview of two important functions for describing random variables, the cumulative distribution function (CDF) and probability density function (PDF).

Gaussian Random Variables

10/26/13

Running Time: 9:53

Examines the PDF and CDF of Gaussian random variables.  Also, discusses other functions related to Gaussian random variables such as the Q function, error function, and complementary error function.

Multiple Random Variables

10/26/13

Running Time: 8:29

PDF and CDF concepts for a single random variable are extended to multiple random variables.  This yields new quantities such as joint distributions, conditional distributions, and independent random variables.

Mean, Variance, and Moments

10/26/13

Running Time: 9:11

Defines the mean, moment, variance, and central moment of a random variable.  All of these quantities are computed using a weighted average of the random variable probability density function.

Gaussian PDF Example

10/28/13

Running Time: 6:56

Examples performs several computations with a Gaussian random variable.  Specifically, the Q-Function is used to compute the probability of the Gaussian random variable being less than or greater than a number.

Mean and Variance Example Computations

11/15/13

Running Time: 7:23

This example investigates a continuous random variable X with associated probability density function p(x).  The mean, mean-squared, and variance of the random variable are computed from the definition (i.e. taking the appropriate weighted average of the PDF).