Mathematics - 2019-10-31 (page 1 of 3)

user193319

00:16

What is the statement of Schur's lemma for Lie algebras? Every source I come across just gives a statement of Schur's lemma for representations of Lie groups and says an analogous statement holds for Lie algebras; but I'm not sure how to translate things from Lie groups to Lie algebras.

Stan Shunpike

00:36

Hello

I was mixing up sets with subsets of sets. In particular, I had mistakenly thought that the real numbers contained the empty set.

I don't understand why probability spaces use the empty set though. For example, what happens when I have a random variable? If probability spaces have an empty set, what does it map to?

Ted Shifrin

Yikes @Stan

Probability spaces are measure spaces, and the empty set is a measurable set with measure 0.

MatheinBoulomenos

@user193319 if $A$ is an abelian category and $V_1,V_2 \in A$ are simple objects in $A$, then every morphisms $f:V_1 \to V_2$ is either $0$ or an isomorphism. Consequently $\mathrm{End}(V_1)$ is a division ring

Ted Shifrin

hi @Mathein

Stan Shunpike

@TedShifrin yikes sums up my relationship with math as of late but that's ok

Ted Shifrin

LOL ... you don't appreciate my critiques.

Stan Shunpike

00:41

oh no i do

MatheinBoulomenos

Hi @Ted

Ted Shifrin

I was trying to get you thinking more conceptually about linear algebra, as opposed to relying on brute-force computation.

Stan Shunpike

it was more that i was frustrated with how slowly i've proceeded at linear algebra

user193319

@MatheinBoulomenos Any way to state it without category theory? I'm just a mere mortal thinking about Lie algebras.

Stan Shunpike

that's why i've been putting in more time

Ted Shifrin

00:42

Linear algebra, done right, is interesting and challenging.

Stan Shunpike

cuz it's showing up in one class and i can tell i'd get a lot more out of it if i went through ur book like im doing now

MatheinBoulomenos

@user193319 no offense, but how hard did you search? it's even on the wikipedia page for Schur's lemma

Ted Shifrin

But mostly it's done wrong (in the US, anyway).

MatheinBoulomenos

Schur's lemma

In mathematics, Schur's lemma is an elementary but extremely useful statement in representation theory of groups and algebras. In the group case it says that if M and N are two finite-dimensional irreducible representations of a group G and φ is a linear transformation from M to N that commutes with the action of the group, then either φ is invertible, or φ = 0. An important special case occurs when M = N and φ is a self-map. The lemma is named after Issai Schur who used it to prove Schur orthogonality relations and develop the basics of the representation theory of finite groups. Schur's lemma...

Stan Shunpike

@TedShifrin that's why i'm doing this in addition to my studies because i want to get the most out of my classes next quarter

and just doing linear algebra during break won't be enough

i need a solid few months doing it everyday

Ted Shifrin

00:43

I think that's not a bad idea.

Did you get the point of my last email?

Meow Mix

Hiii

Ted Shifrin

Oh, look, it's Meow.

user193319

@MatheinBoulomenos Sorry...I was looking through the books I own.

Meow Mix

I miss this place

Stan Shunpike

@TedShifrin No, but I think I just have to struggle with it. I'm gonna reply sometime in the next 24 hours. I'm prepping for a midterm and wanted to clarify my probability notes, but i think i'll wait til break to go over the measure theory sections. Ok I'm gonna run and get back to work. I'll message you later. au revoir mon ami

Ted Shifrin

00:48

A bientôt, @Stan.

aww, @Meow. No one banned you.

Meow Mix

Lol but I have no time for recreational math anymore

Ted Shifrin

Recreational? Hrumph.

What are you so busy doing now?

Meow Mix

School work

Junior year is stressful

Ted Shifrin

Learning anything interesting/challenging?

Meow Mix

Yeah AP chem is offering me a nice challenge

I think chem is really hard

Ted Shifrin

00:50

Well, that's good. Why?

Meow Mix

Everything is just so complicated. Like there's so much more to something so simple like bonding than just "two atoms connect"

And no matter how in depth you go, for a high school course there will always be a point where you just have to accept that that is just how things are instead of looking further into why that's the ase

it's*

So I think it frustrates me in that aspect but it offers a unique challenge

user193319

@MatheinBoulomenos How do I use Schur's lemma to conclude that for simple Lie algebras over $\Bbb{C}$ the space of invariant bilinear forms is at most $1$-dimensional? Is this space a subspace of $hom_{\frak{g}}(\frak{g} \times \frak{g}, \Bbb{C})$ or $hom_{\frak{g}}(\frak{g} \otimes \frak{g},\Bbb{C})$?

Ted Shifrin

Well, I was only truly satisfied about a lot of those things when I took physical chemistry in college.

In high school, a lot of the things are just axiomatic ...

MatheinBoulomenos

@user193319 it's isomorphic to the latter

Meow Mix

I can't wait for that. I hate feeling like I'm so incompetent because I don't understand why something is the case

MatheinBoulomenos

00:54

$hom_{\frak{g}}(\frak{g} \otimes \frak{g},\Bbb{C})=hom_{\frak{g}}(\frak{g},\frak{g}^*) \cong hom_{\frak{g}}(\frak{g},\frak{g})$

Ted Shifrin

Meow, stop taking everything personally.

Semiclassical

A good example of “where does that come from” in chem is drawings of molecular orbitals (s,p,d etc)

It’s easy enough to splash those images in an intro chem book

Ted Shifrin

Well, no one says that the Bohr model is "right." :P

Meow Mix

Aren't those just solutions of Schrodinger's equation things?

Semiclassical

But to actual derive them in QM you need to solve the Schroedinger equation in spherical coordinates

MatheinBoulomenos

00:56

@user193319 the first equality is the Hom-tensor adjunction, the second uses the fact that $\mathfrak{g} \cong \mathfrak{g}^*$ since $\mathfrak{g}$ admits a non-degenerate invariant bilinear form (e.g. the Killing form)

Semiclassical

@MeowMix right

Spherical harmonics and all that

Ted Shifrin

@Semiclassic: But by symmetry doesn't it reduce to just 1-D?

Meow Mix

Everything in physics and chem seems like just a huge mess of a bunch of super tiny things interacting with each other at every point in time and properties just arise from that

Semiclassical

@TedShifrin no

Meow Mix

And I think it's cool it just makes things super complicated

Ted Shifrin

00:57

Hmm.

Meow Mix

But yeah they put me in Calc III this year so math is a bit of a challenge I guess too

Ted Shifrin

In a college?

Semiclassical

To be clear, this is what I have in mind: en.m.wikipedia.org/wiki/Spherical_harmonics#/media/…

Meow Mix

No they teach Calc III at my high school

Ted Shifrin

I guess I meant $\rho$ as a function of $\phi$, @Semiclassic.

Oh, those courses are almost always disasters. Is the teacher actually competent?

Meow Mix

00:58

It's not very rigorous and it kind of frustrates me

She is somewhat competent

MatheinBoulomenos

if $\mathfrak{g}$ is simple, then $\mathfrak{g}$ is an irreducible representation (well actually $\mathfrak{g}$ is abuse of notation for the adjoint representation here

Ted Shifrin

Even most college Calc III courses are bad.

Meow Mix

Yeah :(

user193319

@MatheinBoulomenos So, if $\frak{g}$ is simple, then we conclude that $hom_{\frak{g}}(\frak{g},\frak{g})$ is $1$-dimensional?

Ted Shifrin

No, it can still be a good course without being totally rigorous.

MatheinBoulomenos

00:59

@user193319 yes

Ted Shifrin

But there are difficult concepts that need to be explained, even if we don't talk carefully about what continuity and differentiability mean. (You can always watch my lectures for those, Meow, in your spare time. Ha.)

Meow Mix

I know but when things aren't rigorous I get the sense what I'm doing is shaky

user193319

So I need to how that $hom_{\frak{g}}(\frak{g},\frak{g})$ is an irreducible representation

MatheinBoulomenos

no

Ted Shifrin

@Meow: I can send you my lecture notes from the multivariable calc class at MIT I taught back in 1981. If you are interested.

Meow Mix

01:00

I still remember everything I learned from Spivak's so I feel like I have a solid understanding of Calc I

user193319

How do I apply Schur's lemma then? Schur's lemma is about irreducible representations

MatheinBoulomenos

$\mathrm{hom}_{\mathfrak{g}}(\mathfrak{g},\mathfrak{g})$ is not a representation

Meow Mix

How in depth are the lecture notes

Ted Shifrin

You never got very far in Spivak, @Meow.

Semiclassical

there’s a line I like: “Teaching is the art of telling smaller and smaller lies.”

Meow Mix

01:01

I got somewhat far, like chapter 16

Ted Shifrin

Oh, you never talked to me about anything after Chapter 4.

MatheinBoulomenos

@user193319 you apply it to $\mathfrak{g}$ itself (as I said that's abuse of notation for the adjoint representation, but everyone seems to do that)

Meow Mix

@Semiclassical Haha that's a good one

@TedShifrin Yeah I read up to the trig functions chapter

Semiclassical

The balance, of course, is that if you tell too big a lie then you lose credibility

Ted Shifrin

Reading without doing exercises ?

Meow Mix

01:02

No I was doing exercises

user193319

@MatheinBoulomenos hmm...how do you even define $hom_{\frak{g}}(\frak{g},\frak{g})$...I just realized that I'm entirely certain how to define it.

Ted Shifrin

@Meow: I explained concepts carefully and did examples, but I only did proofs when they gave insight and understanding. It was not a proof-based course. For that, you need my videos.

Semiclassical

So even if it’s not “truly” rigorous it still needs to stand up to scrutiny

Meow Mix

And I think it's important to make it clear when you're telling lies @Semiclassical

Semiclassical

Well

Ted Shifrin

01:04

Not always.

MatheinBoulomenos

@user193319 if $V$ and $W$ are representations of $\mathfrak{g}$, then a $K$-linear map $f:V \to W$ is said to be $\mathfrak{g}$-equivariant if $f(Av)=Af(v)$ for all $A \in \mathfrak{g}$, $v \in V$

Semiclassical

If you tell them you’re lying, you’re not lying :P

Ted Shifrin

Not every course in calculus should be aimed at Spivak-capable students. That would be an unmitigated disaster.

user193319

And $hom_{\frak{g}}(V,W)$ is the collection of all such $f$?

MatheinBoulomenos

yes

Meow Mix

01:05

Yes

Semiclassical

That said, you should always be prepared to admit the lie

Meow Mix

I suppose

MatheinBoulomenos

so teaching is basically lie theory?

user193319

@MatheinBoulomenos So when we write $hom_{\frak{g}}(\frak{g},\frak{g})$, we must have some natural representation of $\frak{g}$ in mind, no?

Ted Shifrin

I knew you were going to say that (or semi would), @Mathein.

MatheinBoulomenos

01:06

@user193319 as I already said $\mathfrak{g}$ is used for the adjoint representation of $\mathfrak{g}$

Meow Mix

Anyways I come here because I have the opportunity to take linear algebra and diff eq next year at a local college and I don't know if that's a good idea. I know if I don't do that I'm not gonna have any math classes and I won't have any motivation to learn on my own

Semiclassical

As in, if someone questions it, it isn’t a good idea to dig in your heels and insist that they’re being silly

user193319

@MatheinBoulomenos That is, $ad : \frak{g} \to \frak{gl}(\frak{g})$ given by $(\text{ad } x)(y) = [x,y]$?

Ted Shifrin

@Meow: It's OK to wait until you actually go to college.

MatheinBoulomenos

yes

Ted Shifrin

01:08

Diff eq is probably OK, but I am sure I'd hate the linear algebra class.

Semiclassical

But you can’t spend all of the lecture repeatedly saying “it’s actually more complicated than what I’m saying”

MatheinBoulomenos

if you do linear algebra at a local college, it's probably over a local field

Ted Shifrin

spanks Mathein

Semiclassical

Depends on what level of linear algebra one is doing. There’s some parts of it which go very nicely with diff eqs

Ted Shifrin

Yes, but no one teaches them combined ... well, it's a set of measure 0.

Semiclassical

01:11

Aye. But if one is doing self-study then there’s at least some parts of linear algebra that goes well with DEs

MatheinBoulomenos

I liked that we did the STFGMPID in in linear algebra

Akiva Weinberger

This thread

https://www.reddit.com/r/math/comments/dpbkwl/graduate_algebra_classes_in_a_nutshell/

Meow Mix

Hi @Akiva

Semiclassical

It does depend a lot on what level of linear algebra one is talking about of course

Akiva Weinberger

> Complex analysis: suppose f(z) is a function which is interesting in some way. Then f is a constant function.

Ted Shifrin

01:12

LOL

I guess I don't agree on the definition of "interesting."

Semiclassical

I very much do -not- have in mind what Mathein would mean by a linear algebra course :P

Ted Shifrin

No, @Semiclassic. He's very pure-math European.

Akiva Weinberger

> Graduate algebra classes in a nutshell
Definitions: take the largest class of objects where everything works the way you want them to.
Theorems: everything works the way you want them to.

Semiclassical

Right.

Akiva Weinberger

First comment

>Definition: Take the largest class of objects that seem to act the way we want.
Example: They sometimes still don't act the way we want.
Definition: An object is called "normal" if it _really_ does act the way we want.

@MeowMix Hey, long time no see

Leaky Nun

01:13

@AkivaWeinberger true

Semiclassical

@AkivaWeinberger easiest counterexample to that are functions with branch points

Akiva Weinberger

@LeakyNun Hey, short time yes see

Meow Mix

I wanna know why that way of computing inverse matrices works

Jacob McMichael

Yo

Meow Mix

Apart from "when you calculate it it gives the identity matrix"

Semiclassical

01:14

@MeowMix which?

Ted Shifrin

Look at my book or videos, @Meow.

Meow Mix

The one where you do like 4 steps

MatheinBoulomenos

Here's a challenge. Which part of math is this theorem from "Regular implies normal"?

Akiva Weinberger

Many

Meow Mix

Like take the cofactors and transpose and whatever

Semiclassical

01:14

That’s...not very descriptive

Oh

Ted Shifrin

Oh, that's a terrible way to find inverses, @Meow, but it's not hard to prove.

Semiclassical

Adjugate matrix

Akiva Weinberger

@MatheinBoulomenos Call a branch of math "perfectly normal" if regular implies normal

Meow Mix

Wait what are the matrices that preserve normals

Adjoint?

Ted Shifrin

Better way is with row operations, @Meow. But proofs of both are in both my books and my lectures.

normals?

Jacob McMichael

01:15

Math is fun

Meow Mix

I had to use that in one of my 3d graphics programs

Semiclassical

Adjugate matrix is nice for theoretical purposes but not for computational

Ted Shifrin

You mean preserve lengths?

Akiva Weinberger

Basically try multiplying them together and see what happens

Meow Mix

No

So like

Jacob McMichael

01:16

I had to use a sinusoidal model to weave around bad data recently. I’m hooked on learning math now

Meow Mix

If you have 3 vectors that form a triangle with normal $n$, the image of those 3 vectors under the linear map form a triangle whose normal is the image of $n$

Jacob McMichael

I am a sponge

Meow Mix

Does that make sense

Ted Shifrin

So the matrix will end up having to be a scalar multiple of an orthogonal matrix.

Akiva Weinberger

I don't know what the context is but I'm imagining a sine wave literally "weaving" around points in the x-axis

Ted Shifrin

01:17

It needs to preserve angles.

Jacob McMichael

Are you putting $ signs there or is that a symbol my phones isn’t picking up

MatheinBoulomenos

we just like money

Akiva Weinberger

tinyurl.com/cfqcvpc @JacobMcMichael

See on the top right ^^^>>>

Semiclassical

On the note of data analysis, there was an op-ed in the Minneapolis paper today

Let me find it

Meow Mix

Oh it's just called a normal matrix

Akiva Weinberger

01:18

Minneapolis - don't they just call it an oped over there

Ted Shifrin

Hmm, normal means $AA^* = A^*A$.

Akiva Weinberger

or an ope for short

Meow Mix

Well here I'm specifically talking about 4D transforms where one coordinate is homogeneous

So that you can do translations and stuff

Jacob McMichael

It’s not working on mobile akiva

Ted Shifrin

If it's real, star means transpose, and then I think it's what I said.

Akiva Weinberger

01:19

I've got it working on iOS Google Chrome

Ted Shifrin

Right.

Akiva Weinberger

There's a way to add bookmarks but it's annoying

MatheinBoulomenos

what does it mean for one coordinate to be homogenous? I know homogenous coordinates for $\Bbb P^n(k)$, but a single coordinate?

Ted Shifrin

No, he didn't mean that, @Mathein.

Semiclassical

m.startribune.com/…

Ted Shifrin

01:20

They're working projectively so that translations become linear.

Jacob McMichael

Yeah I feel that about the money though. I’m heavily into stock forecasting and making new models. But I’m getting tired of it I really want to make sim games lol

Semiclassical

“ Modern high school math should be about data science”

Ted Shifrin

He meant to add an extra coordinate and homogenize. But he didn't say it right.

Yeah, a bunch of my math friends have been debating that seriously on FB, @Semiclassic.

Basically, high school math has become stat to a very large extent anyway.

Jacob McMichael

I’d have to figure it out I’m not in the mood to troubleshoot my iPhone X right now

True semi

Ted Shifrin

OK, I need to go cook dinner. Bubye, all.

MatheinBoulomenos

01:22

here we do calc and linear algebra in high school, but not much stats

Jacob McMichael

Stats is extremely useful

With a GARCH model you can make extra data that looks just like stock market data so if you take all the data yahoo finance offers you can basically use that to make an infinity size sample size

Then run different tests on it to try to make money

Semiclassical

my main issue with that editorial is that calculus is part of what makes data science...well, science

If you don’t understand the tools you’re using to analyze your data, you’re liable to not recognize when those tools are failing

Jacob McMichael

Yeah I agree

Semiclassical

If you want to do serious data science, you need more math not less. a different subject focus, perhaps

Jacob McMichael

Are you into data science I’m guessing

Semiclassical

01:28

Not as such—I did theoretical physics

Jacob McMichael

It’s almost the same thing just add in some python or R and you’re a data scientist lol

Semiclassical

The following does seem to be true, though: most of data science seems to be optimization problems

And the idea that you could understand that without calculus is rather absurd

Jacob McMichael

Yes I want to find out how many people are into in seriously I’m curious

Understand what

Semiclassical

Understand how to solve optimization problems

schn

Consider the proof of the following multivariable chain rule. What happens to the $E(h,k)$ term when dividing by $\sigma$ as highlighted in the red box?

Jacob McMichael

01:34

Just slap a bunch of time series data into excel to where it looks like t(subscript 0) and then t(subscript 1)

loch

I think they're probably just emphasising more on basic statistics (as they said - they want people to know how to use spreadsheets / understand difference between correlation and causation) -- presumably something about hypothesis testing etc.

Jacob McMichael

Then you can forecast different methods. Any math you can think of

loch

but also i do know people who wants to learn calculus after they became aware of it via ML - so it probably would help in motivating more people to learn calculus given the ML hype..

Jacob McMichael

I recgongnize sigma and the v is rho I think

Yes loch that is true sadly

MatheinBoulomenos

you can forecast any math you can think of with excel?

Jacob McMichael

01:37

I only just became motivated to learn math when I found a use for it but I’m sold now

Leaky Nun

@MatheinBoulomenos a regular integral domain is normal

Jacob McMichael

Yes with stock market data from yahoo you can get it from R studio crab repository “BatchGetSymbols”

Then just set it up in excel to study

But I’m struggling because the regular market indicators that are on the internet don’t work or barely work to the point of it’s not worth your time

MatheinBoulomenos

@LeakyNun have you introduced Galois-Brauer descent in your Lie groups class?

Leaky Nun

@MatheinBoulomenos leider nicht

Jacob McMichael

So I basically want to try custom stochastic calculus indicators and test for a better for to the positive returns

MatheinBoulomenos

01:40

sad

Jacob McMichael

I’m sorry if I’m interrupting

MatheinBoulomenos

@LeakyNun I'm TAing intro abstract algebra. Should I tell my students that a semidirect product is a 2-colimit?

Leaky Nun

yes

MatheinBoulomenos

okay

Jacob McMichael

I’m finding out that everyone here is highly into math

MatheinBoulomenos

01:46

surprisingly, given that this is a math chat

Jacob McMichael

Your sarcasm is squared

Anyone here watch Sentdex’s channel?

m.startribune.com/… I see that

genescuba

02:17

0

Q: Covariance between number of tosses to get heads and number of tosses to get tails

Let $X, Y$ be the random variables which respectively are the number of tosses to see your first head and number of tosses to see your first tail. What is the the covariance of $X$ and $Y$ $\mathrm{Cov}(X,Y)$

covariance

If anyone is familiar with covariance

Jacob McMichael

It’s the exact same thing as correlation

MatheinBoulomenos

just take the variance in the opposite category

Jacob McMichael

It’s basically the real word or og word for correlation haha

I’m sure the awnser is a covariance of .5 assuming a 1 means it’s perfectly correlated

Perfectly Positively correlated I should say

Ultradark

speaking of dual categories, does the dual category of representable functors ever project into locally ringed spaces?

genescuba

my question here is I know that cov(X,Y) $=E[XY] - E[X]E[Y]$

$E[X] = E[Y] = 2$ in a fair coin

But how can I think about $E[XY]$?

Semiclassical

02:30

@genescuba should that be 1/2?

More to the point, what are the outcomes?

Jacob McMichael

The chat isn’t rendering the signs I’m new to the mobile version and I tried safari and chrome

Ultradark

click show bookmarks

Semiclassical

Getting it to work on mobile is a bit more annoying, yeah

Ultradark

oh nvm

Semiclassical

You can save bookmarks in mobile safari, though

genescuba

02:32

@Semiclassical why $\frac{1}{2}$

Ultradark

I have yet to get the dollar signs on mobile

genescuba

what is $XY$

Semiclassical

@genescuba well, why 2?

Jacob McMichael

I’m gonna figure this out

genescuba

so $E[X]$ is 2 because we have 1/2 chance of getting heads

Jacob McMichael

02:33

Steve Jobs strikes back from the dead

genescuba

and multiplying 1/2 * 2 gives us 1 which is like flipping twice to see 1 head

Semiclassical

What are your outcomes, ie what value are you assigning to heads vs tails?

Ultradark

$$ \sum_0^1 f(n)? $$

can I do that?

Semiclassical

Without values for your outcomes, it makes utterly no sense to talk about an expected value

Akiva Weinberger

Yoo

Team Trees is already more than halfway to their goal

Ultradark

02:35

YOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

Semiclassical

yo ho yo ho

Akiva Weinberger

Two people have donated a million trees

(Elon Musk and Tobi Lütke, CEO of Shopify)

Ultradark

we're going extinct by 2050

genescuba

@Semiclassical so I guess when I am looking at $E[X]$ tails will be 0 and heads will be 1 right?

and the opposite when I look at $E[Y]$

Semiclassical

Why opposite for tails?

Jacob McMichael

02:37

I freakin put the MathJax code into the bookmark

It still won’t give me the latex

Akiva Weinberger

And you clicked on the bookmark while on this page?

Jacob McMichael

Oh you’re a g

Akiva Weinberger

It's working?

Test: $\displaystyle\sum_{n=1}^\infty\frac1{n^2}$

Ultradark

$$

Akiva Weinberger

¥¥

Jacob McMichael

02:40

I’m not sure how to execute the bookmark from this chat page

😅

Semiclassical

@genescuba from what you’ve said so far, there’s no particular reason to assign 0/1 to tails/heads for X but opposite for Y

Ultradark

$$ |1+1+1|+|1+1-1|+|1-1+1|+|1-1-1|+|-1+1+1|+|-1+1-1|+|-1-1+1|+|-1-1-1|$$

Akiva Weinberger

18?

Ultradark

I'm still calculating it

Jacob McMichael

I did it I am the best

Akiva Weinberger

02:41

Broke: smoke signals

Woke: shine language

Jacob McMichael

I can read

I’m woke now

Semiclassical

It won’t change the magnitude of the correlation but it will change whether X and Y are positively or negatively correlated

Akiva Weinberger

Yay! $\phantom{So you can't see this then}$

Jacob McMichael

Right

Akiva Weinberger

What?

Ultradark

02:42

he said right to semiclassical

Akiva Weinberger

lol

Jacob McMichael

I don’t know what’s going on semi sounds right

Akiva Weinberger

Oh and if you want to undo it you can refresh the page

Jacob McMichael

Yeah no

But thanks for the heads up

Semiclassical

you will have to renew the bookmark if you leave the page

genescuba

02:43

well so for $Y$ we want to count tails rather than heads right so don't we switch

Akiva Weinberger

Fun fact: the sign for "siblings" in Japanese Sign Language is the middle finger

genescuba

so for X I am saying 0:tails and 1: heads and for Y I am saying 0:heads 1:tails

Semiclassical

@genescuba Are you -told- to do that?

If so, fine.

Akiva Weinberger

Jacob McMichael

Gene what is this for

Semiclassical

02:45

But right now you haven’t actually said what X and Y are supposed to represent

Jacob McMichael

The funnest game of coin toss ever

Akiva Weinberger

> A musician was wandering in the jungle when he came upon a clearing that seemed to have acoustical merit. He prepared his violin and began to play.
The music was so beautiful that the wild animals started to gather, they lay down and they all listened. Even the predators were soothed by the music.
Suddenly out of the brush appeared a leopard, he pounced on the musician and tore him to pieces.
A lion asked the leopard “Why in the world did you do that?”
The leopard replied “Huh?”

Took me way too long to get that

Jacob McMichael

What he was hard of hearing?

I don’t understand your math jokes

Akiva Weinberger

Def Leppard

Jacob McMichael

😠

Oh yeah that plane went over my head

Well how long have you guys been here

genescuba

02:49

sorry for the confusion @Semiclassical

Let 𝑋,𝑌 be the random variables which respectively are the number of tosses to see your first head and number of tosses to see your first tail. What is the the covariance of 𝑋 and 𝑌

Akiva Weinberger

I've known about this site for a few years

if that's what you mean

Ultradark

$\approx 1$ year

Jacob McMichael

How much math have you learned

Ultradark

1 unit

Jacob McMichael

1 unit of math haha?

Akiva Weinberger

02:51

Some people here helped me through a textbook

Jacob McMichael

Dang that’s a lot. I saw some people posting about topology I think earlier I’m not sure if I can relate any time soon hahaha

Yo gene a coin toss is random so that means your awnser is uncorrelated or .5

I’m trying to get to stochastics and mabye complex analysis then I can branch into statistics like I need to

Then it’s back to the data bases and crunching numbers trying to get that alpha in finance

Semiclassical

@genescuba ok. Note that the outcomes of X are 1,2,3,4,...

And same for Y.

genescuba

Yup

so @Semiclassical Im having trouble thinking about $E[XY]$

what does $XY$ represent here?

Jacob McMichael

ocw.mit.edu/courses/electrical-engineering-and-computer-science/…

Semiclassical

Before that, let’s make sure you have EX and EY right

genescuba

02:56

Sure

Semiclassical

What are the probabilities for X=1,2,3,...?

Jacob McMichael

eleccompengineering.files.wordpress.com/2015/03/…

Thats the end goal those 2 books right there

genescuba

hmm so for $X$ = 1 its 1/2

and then for 2 its (1/2)^2, 3 its (1/2)^3 and so on

Jacob McMichael

Electricity and robots baby

Semiclassical

Right. So how do you compute EX?

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$Mathematics$ Mathematics