The lecture begins with the axiomatic definition of a random experiment and ends with a few examples in probability. The audio may clip at certain points, but is just an aid to the slides which contain the entire script.

In this lecture, we discuss the very fundamentals of the random variable concept.

In this lecture, we define the C.D.F. and look at some examples.

This lecture provides an overview of the properties of the CDF, with proofs.

This lecture defines the pdf on the basis of the cdf and looks also at the conditional version.

We look at an example of the conditional CDF. The example is elaborate with several cases. We look at each case in detail.

In this lecture, we study the bivariate distribution that is used when we are considering two random variables jointly. We also look at some of its properties.

We look at the definition of joint density in terms of the joint distribution function and vice versa. We look at marginal statistics.

Herein we study independence of two random variables and connect it to the joint CDF and joint PDF.

We discuss in detail two examples of conditioning the cdf and pdf on a set or event.

In this lecture we derive the form of the total probability theorem using Bayes' theorem and conditional, joint and marginal densities.

We define the mean of a random variable based on its pmf (if discrete) and pdf (if continuous).

Herein, if we take a random variable X and form some new random variable Y = cos(X) say, then the problem of finding the mean of Y is addressed.

In this lecture, we discuss how to form the conditional expectation and also a key property of the conditional expectation.

In this lecture we see the definition of random vectors, their pdf and cdf. It will be useful for discussions about random processes.

In this lecture, we extend the concept of independence from events to random variables.

The video provides a deep dive into Lecture 3.