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Fundamentals of Probability Theory

Fundamentals of Probability Theory (1/12): Introduction


Running Time: 2:43

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

Fundamentals of Probability Theory (2/12): Events


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.

Fundamentals of Probability Theory (3/12): Conditional Probability Example


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.

Fundamentals of Probability Theory (4/12): Binary Symmetric Channel


Running Time: 6:31

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

Fundamentals of Probability Theory (5/12): Repeat Coding


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.

Fundamentals of Probability Theory (6/12): CDFs and PDFs


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).

Fundamentals of Probability Theory (7/12): Gaussian Random Variables


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.

Fundamentals of Probability Theory (8/12): Multiple Random Variables


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.

Fundamentals of Probability Theory (9/12): Mean, Variance, and Moments


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.

Fundamentals of Probability Theory (10/12): Gaussian PDF Example


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.

Fundamentals of Probability Theory (11/12): Mean and Variance Example Computations


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).

Fundamentals of Probability Theory (12/12): Received Signal Distribution


Running Time: 12:35

Polar signaling uses a single pulse shape to transmit binary information (i.e. bits) by using positive/negative pulse amplitudes to convey bit information. The receiver can decode the original bit information by sampling the received pulse and decoding to a binary 0 or 1 depending on if the received sample value is negative or positive. This problem derives the density function of the received signal sample values in the presence of additive white Gaussian noise.