Probability Notation Explained

Probability theory often confuses students. This is because the notation is often highly abbreviated and mathematically sloppy. In this video we discuss a few mathematical concepts underlying this notation, scrutinizing a common equation found in an introductory probability course.

Thanks for Russell Shannon and the rest of UCSB's Instructional Development team for the use of their Learning Glass!

To learn more, see Stanford's Sanjay Lall's excellent Engineering 207B course:

(c) 2015 Justin P. Pearson. All rights reserved.

[jacobweaver]

Finally, someone with enough know-how to call out all the professors on their BS. They kill us for not using enough references but they constantly abbreviate beyond understanding and into complete ambiguity.

[cloudgalaxy]

Can we please have a new way of writing and learning probability? Cause I'm fairly confident that no one is learning this stuff from first principles or axioms, and instead is just practicing until their black box in their head gets an intuition.

We need to grow up, I think.
Thanks for your video. I thought I was going crazy.

[jonathansmith]

The probability is not as hard as notation. Would it be possible to include advance notations also ?

[ave]

Thank you so much for this. My probability class seems to think the homework is the best place to even introduce some of this notation. Feels like by the time I figure out what they're asking I could've already solved it. This is super helpful

[realworldprogramming]

This video is so great! I find the statistical notation provided in my classes to often be confusing, and often it is just because it is shorthand for something else that is more meaningful. I would love if you know of any more resources explaining various shorthand in probability and statistics.

Also, I find the explanation you provide of random variables as functions to be very useful. One question I had was in regards to random variables in linear regression. The data points (X1, Y1), (X2, Y2), ... (XN, YN) are all composed of random variables. It seems confusing to think of these as functions. Instead, I have thought of random variables as "the output of a random process". I would love any clarification regarding this topic!

[maegodragon]

You summed up my Problem in the first instance!

[manuelkarner]

wow, big thank you for this video
finaly i found a good explanation & answers to all my questions... & i already consumed a lot of "content" on this

[Qongrat]

Thank you so much for this! Stats becomes quite simple, the only problem is understanding notation - this helps a lot.

[nomercysar]

This is exactly what I was looking for. Thanks a lot for your effort!

[ailishigwedha]

Thanks for sharing this invaluable knowledge. Your explanation is very helpful.

[ianwinters]

I'm doing a refresh of probability and stats, and the notations were killing me. Thank you for making this!

[jackjohnson]

Great, thoroughly informational video. Horrific marker squeaking in the beginning.

[KiranMantri]

awesoooome !! very very helpful ! thanks a lot !!

[chetanaik]

Are you writing these on a mirror, or have you learnt how to write mirrored and are using a transparent board?

[medicinalvl-up]

Great lecture!! Love it!
Btw you look like the cop from the netflix series "the Ozarks"

[frycomfort]

Have to say Doc the way you talk reminds me of Elon Musk and it is amazing!

[alexbierut]

the sounds of the marker makes this unwatchable.