daocheny

my math helpdesk hours: Mon 2pm - 4pm Fri 1pm - 3pm (closed during reading break)

this is also why a borel function applied to a lebesgue function is lebesgue (the function on the outside, whose preimage we take first, needs the stronger measurability). also if we assumed that measurable meant borel measurable then compositions will always be measurable.

"composition of measurable functions is not necessarily measurable" is misleading bc it's only true for lebesgue measurable i.e. preimage of borel sets being lebesgue sets, where there's a mismatch between the sigma algebra used on the domain vs the image.

tau is an optional time wrt Ft+ iff it is an optional time wrt Ft- proof: "<=" trivial (Ft- is in Ft+) "=>": note union {tau<t-1/n} = {tau<t}, and each {tau<t-1/n} is in F(t-1/n}+ in Ft- corollary: tau being an optional time wrt Ft+ or Ft- or Ft are equivalent

broke: a stopping time is an optional time under the same filtration enlightened: knowing whether it's too early is stronger than knowing whether it's too late (since too early => not too late, and not too early but too early up to now => not too late, & too late otherwise)

@TiffanyYongTQ i think they use brouwer's fixed pt & some limit stuff to prove some existence results like it's limited but it's there

@daocheny sucks to suck :P (it has analysis??)

someone came to my helpdesk w an algorithmic game theory question & WHY DIDNT YALL TELL ME HOW BASED THAT CLASS IS ("we did" SHUT UP)

just realized my twitter bio always said mcgill '23 instead of '22 hahaha that's so embarassing imagine if i majored in maths

@TiffanyYongTQ i didn't know algo game theory had both prob and analysis 😭

@daocheny ur the one who said you wanted to do prob and stats classes .-.

@TiffanyYongTQ they should announce it officially once they have all the ppls classes that they want to help with

@daocheny where are the helpdesk hours even? i don't see them advertised anywhere can ya'll put it on the SUMS listserv

accidentally put my helpdesk hours as 1-4 instead of 1-3 so y'all get to have an extra hour of prob propaganda

D(theta) doesn't HAVE to be continuous or discrete but since we didn't see conditional probability in ad prob im not gonna try to be fancy & say stuff that's wrong

the formal definition is: Given a continuous or discrete distribution D(theta) taking value in S subset R^n, T : S -> R^m is sufficient wrt theta if for X ~ D(theta), the distribution of X | T(X) does not dependent on theta (one can see this as X | T(X) = X | theta in dist).

i really like the intuition wikipedia gives for sufficiency: a statistic is sufficient wrt a parameter iff any inference of the parameter based on maximum likelihood would be the same if one had the entire data vs only that statistic

the help desk is live until 4 btw a person came & asked for odes help IM SO SAD I COULDNT HELP

woke up at 1 pm, panicked & glad that my help desk hours start at 2 pm COME TO MY HELP DESK!! will help w any prob / stats / linear / analysis (up to 4) (i hope they posted the schedule & stuff already? if not then big rip)

feels like my brain will automatically gain new folds after i understand the proof for azuma's inequality

glm is so cool!! it's the first time ive seen a formal justification for using the logistic function in modelling bernoulli responses

(even though i have seen this in alg 2 already) i finally understood why aren't all unitarily diagonalizable matrices hermitian, since A*=(PDP*)*=PDP*=A: all unitarily diagonalizable matrices w REAL eigenvalues are hermitian, but my dumbass forgot D*=/=D

the intuitive reason why clt works is that the moments of ANY variance normalized sums behave "similarly" as n -> infinity, so if that sum happens to be of gaussians, then the sum will be standard gaussian, so its moments are where the moments of all such sums will converge to.