Відео

This channel is now deprecated. Please find this video on my new channel: ua-cam.com/video/s4XU4ZHTyAM/v-deo.html In this lecture video, we prove the existence and uniqueness of product measure. We then prove Fubini & Tonelli's theorem, which allows us to switch the order of integration. Lastly, we prove existence and uniqueness of probability measures on infinite product spaces.

This channel is now deprecated. Please find this video on my new channel: ua-cam.com/video/8wLfUmhM6YA/v-deo.html In this lecture, we formally define the integral for a measurable function. We then state and prove three very important theorems regarding integrals and limits: Monotone convergence, Fatou's Lemma, and Dominated Convergence.

This channel is now deprecated. Please find this video on my new channel: ua-cam.com/video/2YWdiX2_6y4/v-deo.html In the first half of this lecture, we construct Lebesgue-Stieltjes measure and briefly discuss Radon measures. In the second half, we begin our discussion on product measure. Before proving existence and uniqueness of product measure (lecture 8), we state and prove the Monotone Clas...

This channel is now deprecated. Please find this video on my new channel: ua-cam.com/video/eyWLekPzzuE/v-deo.html In preparation for defining the integral, we introduce the notion of both simple functions and measurable functions. We then state a bunch of useful properties regarding measurable functions. Note that simple or measurable random variables are just simple or measurable functions on ...

This channel is now deprecated. Please find this video on my new channel: ua-cam.com/video/yFZ3N85NIbc/v-deo.html In this lecture, we formally construct Lebesgue measure on the real line by starting with the collection of half open intervals and using the extension and uniqueness theorems from the previous two lectures. We also talk briefly about product measures and independence of sigma-field...

This channel is now deprecated. Please find this video on my new channel: ua-cam.com/video/uSSnwNr0Iec/v-deo.html In this lecture, we prove the uniqueness of extending a measure using the Carathéodory Extension Theorem from the last lecture. The main tool we use is Dynkin's Pi-Lambda Theorem. You can read about pi and lambda systems as en.wikipedia.org/wiki/Pi-system. Written notes can be found...

This channel is now deprecated. Please find this video on my new channel: ua-cam.com/video/NdZnhTMoNnM/v-deo.html In this video lecture, we prove Carathéodory's Extension Theorem. This theorem allows us to take a pre-measure defined on a ring or semi-ring and extend it to a measure on a sigma field. It will be a useful tool for constructing measures such as Lebesgue measure. My written lecture ...

This channel is now deprecated. Please find this video on my new channel: ua-cam.com/video/qnVZku1_a3Q/v-deo.html In this video, we introduce some of the main definitions in Measure theory. This includes measures and sigma-fields and some examples to set the stage for future lectures. Written Lecture Notes can be found at sites.ualberta.ca/~kashlak/kashTeaching.html

Link to my teaching page: sites.ualberta.ca/~kashlak/kashTeaching.html Link to my main website: sites.ualberta.ca/~kashlak/index.html

In this lecture, we quickly review the main topics of this lecture course.

TSA Review Lecture

TSA Lecture 24: The GARCH Process

In our final lecture, we briefly introduce the concept of a cross-over design where a subject is exposed to every treatment over some period of time.

TSA Lecture 23: Exponential Smoothing

DoE Lecture 23: Non-Normal Data in R Studio

TSA Lecture 22: Estimating the Spectral Density III

DoE Lecture 22: Designs with Non-Normal Data

DoE Lecture 21: Plackett-Burman Designs

TSA Lecture 21: Estimating the Spectral Density II

TSA Lecture 20: Estimating the Spectral Density

DoE Lecture 20: Mixed Level Designs and Designing Experiments in R

TSA Lecture 19: Spectral Density and Distribution

DoE Lecture 19: Prime and Mixed Level Designs

DoE Lecture 18: RSM Optimization and R Code

TSA Lecture 18: Periodic Processes and the DFT

DoE Lecture 17: Central Composite Design and more

TSA Lecture 17: Seasonal ARIMA in R Studio

TSA Lecture 16: Seasonal ARIMA Models

DoE Lecture 16: Response Surface Methodology