Convergence and limit theorems 1/12 - Levels of convergence and main properties.

In this video, we define various types/levels of convergence for sequences of random variables: convergence in distribution, convergence in probability, convergence almost surely and convergence in the pth mean. We conclude with a picture showing the implications among all the different types of convergence. These implications will be proved in the next videos of this playlist. This is Section 3.1 of my Stochastic Modeling book.
This video is part of the playlist Advanced Probability • Measure theory and pro... .

[@theprobabilitychannel-prof8089]

This video is part of the playlist Advanced Probability ua-cam.com/video/qGsHiHwgInU/v-deo.html.

[@mrnotfhacof837]

Very helpful, Professor! thank you for uploading this.

[@theprobabilitychannel-prof8089]

I am glad this video helped. Take care.

[@sorenieg3073]

This was great! Thank you!!

[@theprobabilitychannel-prof8089]

Thanks.

[@ridwanwase7444]

Please add subtitle
Your playlists are gems...but hard without subtitles
Best wishes for you.

[@FF-ms6wq]

Thank you for your great videos.
Small question: At 8:20, is it true that we do have to assume that the r.v. X is *independent* from all the X_i ? I think it seems required, and it wasn’t explicitly mentioned. So that’s why I am asking.

[@reyhanehghaderi9179]

you have a lot of accent when you are talking English and your subtitle for writing in English dose not work your videos cannot be useful

[@davidbanahene307]

Learn to appreciate effort