Another great video! Thank you so much for all the hard work you put into this! For viewers and self learners, this is truly a godsend! We look forward to your next video, when able, of course!!
After working through lessons 1 to 19, glad to share that this Measure Theoretic Probability series of lessons has been a valuable resource for me. It shines in ways that differ from traditional pedagogical exposition. In particular, this series doesn't shy away from long-form explanations, repetitions of previously conveyed concepts (which I've found to be pretty helpful for learning abstract, seemingly disparate concepts common in math), and attends to intricate topics at a comfortable pace. As such, I am happily subscribed to this channel (enthused to be notified of video uploads), and placed an order for the lecturer's (Prof. Corcoran) book titled, "The Simple and Infinite Joy of Mathematical Statistics". I may possibly be wrong here - but at 25:32 into this lesson, should it be X_n(ω) = 0, for all n > 1 / (3ω - 2), instead of n > 3ω-2 ? Also, possibly helpful for others who are watching this (not sure if this was mentioned): a.s. convergence is similar to point-wise convergence of a sequence of functions, a fundamental concept that's often touched on in undergraduate real analysis courses. Notice that random variables X_1, X_2, X_3, and so on, are _functions_ that map elements in the sample space Ω to the real line ℝ. As such, one may wish to figure out whether this infinite sequence of random variables (X_1, X_2, X_3, ...) tends to some limiting function (which is frequently denoted with the symbol X in this video lesson).
Another great video! Thank you so much for all the hard work you put into this! For viewers and self learners, this is truly a godsend! We look forward to your next video, when able, of course!!
After working through lessons 1 to 19, glad to share that this Measure Theoretic Probability series of lessons has been a valuable resource for me. It shines in ways that differ from traditional pedagogical exposition. In particular, this series doesn't shy away from long-form explanations, repetitions of previously conveyed concepts (which I've found to be pretty helpful for learning abstract, seemingly disparate concepts common in math), and attends to intricate topics at a comfortable pace. As such, I am happily subscribed to this channel (enthused to be notified of video uploads), and placed an order for the lecturer's (Prof. Corcoran) book titled, "The Simple and Infinite Joy of Mathematical Statistics".
I may possibly be wrong here - but at 25:32 into this lesson, should it be
X_n(ω) = 0, for all n > 1 / (3ω - 2),
instead of n > 3ω-2 ?
Also, possibly helpful for others who are watching this (not sure if this was mentioned): a.s. convergence is similar to point-wise convergence of a sequence of functions, a fundamental concept that's often touched on in undergraduate real analysis courses. Notice that random variables X_1, X_2, X_3, and so on, are _functions_ that map elements in the sample space Ω to the real line ℝ. As such, one may wish to figure out whether this infinite sequence of random variables (X_1, X_2, X_3, ...) tends to some limiting function (which is frequently denoted with the symbol X in this video lesson).
Thanks for the clear explanation. It was very helpful.
Fantastic!
Still here :)
8 months? Hopefully that was an exaggeration.
Yes! 😝 (Hopefully...)
"In like 8 more months" 🦜