Mathematics

Not Tfue

1:34 AM

I think I don't get what P(W<=w) means.

And it also doesn't makes sense what that cdf means.

I get the P(W<=w) means but I don't get what P(W>w) means

Not Tfue

1:52 AM

I think I am confused about that CDF means here for w>=0.

looks like geometric distribution

;_;

and it keeps saying Poisson distribution count no of occurrences I don't see that I see it counts probability or is it talking about that n choose k stuff where we do count them then multiply with their probability

i think it is talking about the input of that pmf

and is $P(no occurrences in [0, w] )=e^{−λw}$ from Poisson I get it that you plug 0 into Poisson but I don't get why take exponent to $w$.

copper.hat

3:57 AM

$P[W \le w]$ is the probability that $W$ is $\le w$.

one potato two potato

4:27 AM

It's surprising that derivative is a covering map between germ spaces

user541396

8:37 AM

Is there any good way to understand the book, "deep learning" by Ian Goodfellow ? The book is quite math heavy, and I don't understand several things. Like how one equation leads to other. Is there a guide book of sorts to help me?
Or is there any other book which can hold my hand while going through math?

Any math book I could read first which will help me through this?

one potato two potato

12:42 PM

math.stackexchange.com/a/1999735/668308 How does the reduced l.e.s. of pair $(X,A)$ ensure $\varphi(X) = \varphi(A)+\varphi(X/A)$?

Jai Sri Krishna

1:31 PM

Are there any books on CG one could prescribe me?

Co-ordinate Geometry*

Not Tfue

1:43 PM

what I don't get is why is $e^{-t\lambda}=P(T>t)$ and not $P(T\let)$

I can only interpret it as 0 success until t but I don't see why it is same as the probability of waiting time until the first success greater than t time unit...

I see it as $P(T=t)$

robjohn

@NotTfue $P(T\gt t)$ is the probability that there are no occurrences in $[0,t]$. That is $\frac{(\lambda t)^0}{0!}e^{-\lambda t}$.

Not Tfue

I see what you did there :)

Thanks

copper.hat

2:17 PM

I would word it as $P[T \ge t+1]$

Thorgott

@onepotatotwopotato $H_n(X/A)\cong\tilde{H}_n(X,A)$

one potato two potato

@Thorgott I know what you're trying to say. But the additivity of rank is for s.e.s. not l.e.s.

Not Tfue

One more question I don't get how you get this formula for probability until k th success.

I tried thinking from 2 success but I don't seem to grasp the idea by just looking the formula.

Shinrin-Yoku

I like the linear algebra proof of the algebraic numbers being a field

copper.hat

2:38 PM

@NotTfue How is that consistent with your formula above $P[T>t] = e^{- \lambda t}$?

Thorgott

@onepotatotwopotato the alternating sum of ranks in any exact sequence starting and ending with $0$ is $0$

the slightly more general fact is that if you have a finite complex $C_{\bullet}$ of f.g. abelian groups (or f.g. vector spaces over some field), then $\sum_i(-1)^i\mathrm{rk}(C_i)=\sum_i(-1)^i\mathrm{rk}H^i(C_{\bullet})$

it's a slightly more elaborate version of rank-nullity

hi @Ted

Jakobian

9

Q: closed unit ball in a Banach space is closed in the weak topology

Let $V$ be a Banach space. Show that the closed unit ball in $V$ is also closed in the weak topology. I know this is a consequence of the statement any closed convex subset in $V$ is closed in the weak topology, which the proof used the geometric Hahn-Banach theorem. My question is: does this ...

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$Mathematics$ Mathematics