help-27

[devout snow]

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[devout snow]

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[weak cove]

I'm confused exactly what the set of points describing a "slab" is

it says I think in the image that the points are

{y in R2 | c<= a^T y <= b }

but

what are c, a^T, and b?

and when it says it can be constructed by intersecting two opposing halfspaces whose bounding hyperplanes are parallel but not coincident

what is a halfspace?

something related to a subspace I assume

[devout snow]

@weak cove Has your question been resolved?

[devout snow]

@weak cove Has your question been resolved?

[uncut crow]

these are the two halfspaces

draw a line in the plane and take all points "below" it

that's an example of a halfspace in R^2

all points above it is another halfspace

my convex optimization sir taught me about halfspaces

[weak cove]

wow I need a convex optimization sir

Do you know about the other doubt I had?

[uncut crow]

which one?

[weak cove]

the beginning doubt of this channel

[uncut crow]

let's start with something simpler, {y in R2 | a^T y <= b }

[weak cove]

Sure

[uncut crow]

a^T and b are fixed

[weak cove]

what is a^T?

is b in R2

[uncut crow]

a^T is just a fixed vector in R^2

b is in R

[weak cove]

Sure

(a1, a2) * (y1, y2) <= b

the set of all (y1, y2) satisfying this for fixed (a1,a2)

[uncut crow]

yea

[weak cove]

Am I supposed to be able to visualize that?

Let's say b is 1/2 or something

and a=(2,5)

[uncut crow]

i have trouble visualizing it just from that but you can see it's equivalent to all points under a line with some algebra

[weak cove]

Sure

and then

c<= a^T b

would then be all points above some other line

[uncut crow]

yep

[weak cove]

how do we guarantee that the lines are

like in proper order

so that we get a slab rather than some unbounded set like the complement of the slab

[uncut crow]

i guess we just need to show the lines are parallel?

and we can assume c<b ig

[weak cove]

Okay

I buy it

Thank you Ma'am

[uncut crow]

thank my convex optimization sir

[weak cove]

have you had any semi-definite programming sirs?

[uncut crow]

my convex optimization sir taught me some linear programming which i think is related

[weak cove]

yes

[uncut crow]

i probably can't help tho

[weak cove]

I badly need a SDP and convex optimization sir

[weak cove]

ever do maxcuts and Goemanns-williamson?

[uncut crow]

no we will do max cuts later in the semester

never heard of the other thing

[weak cove]

it's the best algorithm for finding a lower bound on the max-cut

if u do much better apparently u prove P=NP

but my sir wants us to improve it

there's some wiggle room before P=NP

[uncut crow]

i guess this picture was a little imperfect, both the half spaces should include the blue

and the slab is the intersection of them

[weak cove]

Makes sense

[uncut crow]

you have an intensive sir

[weak cove]

yes he thinks I know much more than I do

I asked him about grading scheme

and he told me if I improve the max cuts

I get a 4.0

[uncut crow]

[weak cove]

I also have the option of failing to improve the maxcuts

but documenting my failure

anyhow it's kind of cool but I'm not as good as my sir

maxcuts is like nearly solved if ur in like all of the complicated cases

but if ur graph is like

almost bipartite

which is nice for the max cut

it's actually

bad

for ur algorithm

idk

u would have to ask my sir

[uncut crow]

i'm making a wordle solver for a project my optimization sir assigned

[weak cove]

typical

solve max cuts instead

and then tell me ho

how

[uncut crow]

he did say something about max cuts to me and my friend when we were talking to him about our project but i can't remember what it was

[weak cove]

What class are you taking

optimization?

[uncut crow]

yea

[weak cove]

I should take that

[uncut crow]

it's pretty cool

[weak cove]

https://math.washington.edu/courses/2024/spring/math/563/a

I'm taking this

idk any optimization and linear programming

so I get confused by my sir alot

[uncut crow]

ic

my convex optimization sir hammers us with a lot of multivariable calculus every day that i never learned

[weak cove]

u should rly not let ur sirs hammer u

I just learned multivariable calculus again and I think I get it this time

[uncut crow]

i understand it ok but i kinda lose the plot when i actually have to work abstractly with partial derivatives and hessians and multivariable taylor's theorem and stuff like that

[weak cove]

hessians aren't real and multivariable taylors theorem is hell

[uncut crow]

writing proofs involving that stuff is hard for me

[weak cove]

Do you have an example proof

I am curious

[uncut crow]

uhh here's a not too complicated one

[weak cove]

yeah looks no fun

ur a tryhard for making ur latex have color btw

.close

[devout snow]

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[uncut crow]

[devout snow]

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[unreal thunder]

consider the ring of 2 x 2 matrices with integer entries.

[unreal thunder]

suppose I= { set of all 2 x 2 matrices with entries which are multiplies of 4}

Q) is I an ideal of R, and further find the cardinality |G/I|

My answer: Yes, multiplying any matrix with a matrix whose entries are multiplies of 4 are again multiplies of 4

thus I is an ideal of R

further, since I is an ideal I absorbs all entries which are multiples of 3

[
R/I= \left{ \begin{bmatrix}
a_1 & a_2\
a_3 & a_4
\end{bmatrix} + I ,\middle|, a_i \in {0,1,2,3} \right}
]

[woven radish]

Dubs

[unreal thunder]

I think the cardinality is 4^4

please check my answer

[devout snow]

@unreal thunder Has your question been resolved?

[unreal thunder]

<@&286206848099549185>

[devout snow]

@unreal thunder Has your question been resolved?

[unreal thunder]

should I rephrase the question?

if in case it's too long to care

Find the number of cosets in R/I, where R is the set of 2 x 2 matrices with integer entries

I is the set of matrices whose entries are multiplies of 4

[stone stump]

well thats not the only property an ideal needs

[stone stump]

imo thats a bit too imprecise

[devout snow]

@unreal thunder Has your question been resolved?

[devout snow]

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[restive river]

it says im wrong, idk what im doing wrong

[restive river]

my notes and my work on the question itself

<@&286206848099549185>

this is the answer they gave

idk how thye got 1/6 instead

[devout snow]

@restive river Has your question been resolved?

[restive river]

The equation for the tangent line needs to get the point when t=1/9

When t=1/9, as x=2t, x will be equal to 2/9 and y=sqrt(t)=1/3

So, at x=2/9, y needs to be 1/3

If the slope is correct, then we have $\frac{1}{3}=\frac{3}{4} \cdot \frac{2}{9} + b$

[woven radish]

Palahoo

[restive river]

So, b is equal to 1/6

[devout snow]

@restive river Has your question been resolved?

[restive river]

ohhhh ur right

i forgot its 2/9 not 1/9

mbmb

thanks!

[devout snow]

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[restive river]

so im doing statistics and confidence intervals, so would I use a z-interval when I know the population standard deviation, and a t-interval when I only know the sample standard deviation?

[inner scarab]

Correct. When you're doing interval about a mean. If you're doing it around a proportion, you'll always use z

[restive river]

thats cool, thanks. additionally does a 20% siginificance level mean a 80% confidence interval?

[inner scarab]

Generally yes. You usually take 100% minus the significance level. Have you done hypothesis tests yet?

[restive river]

yes I have

[inner scarab]

Okay so sometimes you need to be aware of what your alternative hypothesis is. If it's a two-sided alternative, then yes, subtract the sig level to get the confidence level

[restive river]

yeah that lines up with the secnario im working with, thanks

.close

[devout snow]

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[devout snow]

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[warm lantern]

How to find derivative of this??

[warm lantern]

I have done little bit of it

[eager nova]

Show

[robust dust]

that's it

[warm lantern]

This much

[heavy current]

for future reference

[robust dust]

it doesn't simplify any more

[heavy current]

!noclopen

[devout snow]

Please don't repeatedly close and claim a new channel with the exact same question. This erases all previous progress made towards your problem and is confusing for helpers, making it more difficult to help you. Please be patient, even if your channel has not received much attention.

[heavy current]

lmao

[warm lantern]

But in book answer is different

[robust dust]

what is it expecting

[eager nova]

Seems correct

What does your book says?

[warm lantern]

, rotate

[robust dust]

where is a from

[warm lantern]

Maybe book is wrong?

[robust dust]

what's the original question

[eager nova]

Maybe you missed context in your question

[warm lantern]

Different the following with respect to x

[eager nova]

Do a picture like you did with the answer

[warm lantern]

Sure

It's qn.r

@eager nova

[eager nova]

Your answer is correct

[warm lantern]

Okay thank you

.close

[devout snow]

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[devout snow]

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[idle coral]

Does anyone know how to prove these trigonometric identities?

[fossil locust]

Try substituting x = 2u

So you have csc 2u - cot 2u and you want to show it's equal to tan u

Also you should know what csc^2 x - cot^2 x is, so doing csc 2u - cot 2u gives you the other identity for free

[fossil locust]

If you're stuck, write them out in terms of sin 2u and cos 2u

[devout snow]

@idle coral Has your question been resolved?

[idle coral]

:/

[fossil locust]

Let me check

[fossil locust]

Ahhhhh you should have 1 - 1 + 2 sin^2 u

So you're nearly there, just use the identity for sin(2u)

[idle coral]

👍

[fossil locust]

Yeah all good

Nice work

🫡

[idle coral]

thanks, for the second identity it would be almost the same, right?

cot(x/2)=csc(x)+cot(x)

[fossil locust]

Yeah you could try proving it with a similar method

[fossil locust]

Or just this

[devout snow]

@idle coral Has your question been resolved?

[devout snow]

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[restive river]

The lateral surface of the cone after expansion is a sector of a circle with a radius of 12 cm, the central angle is 225. Calculate the total surface area of the cone.

[restive river]

can someone show me if my answer equals desired answer

and how should i calculate to get that answer

[devout snow]

@restive river Has your question been resolved?

[icy barn]

what were u trying to do here?

[restive river]

i thought 7,5^2 is the same as 7x7 + 0,5x0,5 but the results didn't match so i had to check and it came out its not the same XD

[icy barn]

well, the calculation is correct but the only problem is thats not the total surface area

[restive river]

btw i have checked and my results equals the desired one (the orange one) but i still don't know how to do it so i can get the second result

[restive river]

oh yes my bad

it is supposed to be volume of a cone

[icy barn]

u mean, how to simplify ur answer so that u get the orange result?

[restive river]

yes

thats what i mean

oh i just saw i cropped the screen too much, it is supposed to be √87,75

i have found smth like this

but i don't get the first step

can you explain

[icy barn]

the first stip he trys to get rid of the fraction part, which is the .75

[restive river]

ohhh

[icy barn]

cuz 87.75 = (87 + 0.75)
= 87 + 3/4

[restive river]

yes yes now i see

[icy barn]

so u would multiply by 4 to get rid of the 4 down there

[restive river]

what about 4th step

56.25 = 225/4

[icy barn]

same idea
56.25 = 56 + 1/4

[restive river]

oh 🤦‍♂️

[icy barn]

multiply by 4 to become
56*4 + 1

of course, he actually multiply by 4/4 to keep the equation as its

[restive river]

okay i got it now

thank you for help

.close

[devout snow]

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[devout snow]

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[cerulean rover]

Is there a way to solve this without graphing it?

[restive river]

factor x

then do discrimnant

or delta whatever u call it

b^2-4ac

take the two cases

[lusty sapphire]

This is cubic, not quadratic

[restive river]

doesnt matter

[lusty sapphire]

.....

[restive river]

factor x and you will have quadratic

[patent marsh]

Wut

[lusty sapphire]

How are you gonna factor it?

[kindred agate]

mate how do you factor x

thers

theres

theres an 0.7

[restive river]

oh there s no x

[lusty sapphire]

!xy

[devout snow]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[cerulean rover]

I'm doing part B problem 1

It may just be that I need to graph it because I'll need to do that for the next part of the problem anyway, but I wasn't sure

[lusty sapphire]

There is a cubic formula. But it's pretty large, and if you want decimal approximations, then just graphing or using a calculator is all you need to do.

[cerulean rover]

Okay! thanks!

.close

[devout snow]

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[devout snow]

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[spice crow]

is this proof correct to show that L3 isnt a regular language with myhill nerode relation? thanks!

[devout snow]

@spice crow Has your question been resolved?

[devout snow]

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[wary sphinx]

is my process for the 2nd and 3rd question correct? im also having trouble with question 1 when trying to find the x and y component of vector OB

i keep getting inconsistent numbers for the components

<@&286206848099549185>

rip

[devout snow]

@wary sphinx Has your question been resolved?

[wary sphinx]

D:

[devout snow]

@wary sphinx Has your question been resolved?

[devout snow]

@wary sphinx Has your question been resolved?

[devout snow]

@wary sphinx Has your question been resolved?

[devout snow]

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[minor plover]

how do i start

[river prawn]

the hint is telling you to think of the two walls as one wall, how do you think you could apply that?

[minor plover]

um

make it one plane

wait i think i know how to do it without calculus but how do i use caculus here

can someone please help im so confused 😭

<@&286206848099549185> please 😭

i solved it without calculus but how do i use caculus

[rugged sparrow]

think of a cube net

ahh im unsure about calculus as well

[minor plover]

what is that...

[spare crypt]

the calculus way is calling the depth of the corner point you go to x and writing out the distance in terms of x

[minor plover]

oh

ok

how would i continue from there

[spare crypt]

take the derivative and set it equal to 0

should solve to x=2

[minor plover]

wait what am i deriving

[spare crypt]

the blue length

you get the diagonals with pythagorean theorem on my image

[minor plover]

why do i set it to 0

[spare crypt]

just in general if you have some value you want to max/minimize you take the derivative and set it to 0

[minor plover]

ohhh

ok

i got it!

ty!

.close

[devout snow]

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[devout snow]

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[queen tapir]

i must prove that this is right for every a>0

using lagrange mean value theorem

so i have like the answer but didnt understand how it happened

the answer started with f(t)=ln(t) for every t>0

and said that f(t) is continuous in [x,x+1] and derviative in (x,x+1)

and because of those 2 stuff i can use mean value theorem

and that theres c that belongs to (x,x+1)

and so on but like

i didnt understand

why the domain is [x,x+1] and (x,x+1)

why its not [1/x,1/(x+1)]

and why is the x+1 even the b here not a

shldnt it be [x+1,x]?

[floral ridge]

have you tried ln(1+a)-ln(a)=ln((1+a)/a)

[floral ridge]

oh ok

sorry

[devout snow]

@queen tapir Has your question been resolved?

[queen tapir]

np

[bitter spire]

!done

[devout snow]

If you are done with this channel, please mark your problem as solved by typing .close

[bitter spire]

.close

[devout snow]

@queen tapir Has your question been resolved?

[queen tapir]

didnt get the answer yet

[queen tapir]

nvm solved

but got a simple question

now if i have like

x/2 - x^2+x-3/x

when i make the 2 that is down in the first side x

do the equation become x-(x^2+x-3) or x-x^2+x-3

[devout snow]

@queen tapir Has your question been resolved?

[devout snow]

@queen tapir Has your question been resolved?

[devout snow]

@queen tapir Has your question been resolved?

[devout snow]

@queen tapir Has your question been resolved?

[tame wing]

How do you make the first 2 that is down an x??

what are you multuplying by

[queen tapir]

im not sure i just dropped this random example to ask this question

[queen tapir]

.close

[devout snow]

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[devout snow]

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[rapid escarp]

Hi, could someone clarify my answer for this?

[rapid escarp]

I have 700000 of these datas lol

is the "rate" just the timestamp/event?

in that case i have the 100 rates, then is the coefficient of variation the standard deviation of the 100 rates/ average of the 100 rates?

[winter torrent]

i think the rate would be 1 / the difference between the timestamps of two successive events?

[rapid escarp]

Hmm, this was my previous question

I think this gives insight on what "rate" means

[winter torrent]

yeah

the unit should be 1 / sec

[rapid escarp]

shouldn't it be timestamp/event?

it says "rate of signal events per second"

there's 763301 signal events in 318579019 milliseconds

[winter torrent]

yeah so events / seconds

[rapid escarp]

318579019 ms is approximately 318579 seconds

okay so basically

763301/318579 is what i had for this

i guess that's right

so hmm going back to the main question thingy

[rapid escarp]

the rate would be this right?

[winter torrent]

yeah

[rapid escarp]

timestamps = []
for i in range(len(lines)):
    timestamps.append(int(lines[i].rstrip().split() [3]))
average = []
for i in range(100):
    average.append((timestamps[i])/(i+1))

main_average = abs(np.average(average))
main_std = np.std(average)

coeff = (main_std)/(main_average)

#print(coeff)```

so do you think my "algorithm" is right?

i think it's right but like

i didn't get the answer

or at least close enough

my answer was: 0.16864373024776919

am i supposed to answer about 0.1%?

I would thijnk they'd include a choice for 0.2% instead

[winter torrent]

hmm

isn't that 17%?

seems high

[rapid escarp]

wait isn't that 0.1% literally?

0.16%

[winter torrent]

why are we doing timestamps[i] / (i+1)?

[rapid escarp]

I printed the first 5 timestamps:

so like 609/1 + 1891/2 + 2324/3 + ...

[winter torrent]

yeah but like

why

i don't get what that does

[rapid escarp]

isn't that what they mentioned?

"compute 100 rates"

where each of those rates is "signals events per second"

wait

it should be [1/609 , 2/1891 , 3/2324 + ...]?

[winter torrent]

is there some information you're supposed to use to separate these into 100 categories that i'm not seeing here?

[rapid escarp]

nah that's all i have too

what's the confusion?

[winter torrent]

this talks about "these 100 bins"

[rapid escarp]

oh yeah

idk if this was relevant

this was like a uniformly distribution

but yeah that's the only question regarding "bins"

literally no clue how i was supposed to use that

[winter torrent]

hmm

well i guess it wanted you to keep track of how many events happened in each time slice

and then you take the mean / stdev of that array of event counts

[rapid escarp]

what i had in mind was basically this:

I make an array (100 elements) of rates (signals/seconds)

find average of that list

find std of that list

Then do this

[winter torrent]

okay sure yeah

[rapid escarp]

so right now my rate is wrong right i guess

i did time/signals

[winter torrent]

but you need to calculate that array of rates

easiest way to do that is to just count how many events in each bin

[rapid escarp]

calculate what exactly?

[winter torrent]

and then divide by how many seconds that bin represents

events / sec

so like if your bins are 5sec each, and there are 108 events in the first bin, then that has a rate of 20.4 events / sec

[rapid escarp]

can't i just do this?

or am i missing something

this gets me the arrays of [1/609, 2/1981, 3/2324, ...], right?

[winter torrent]

yeah but like

that doesn't help you at all?

then you're only looking at the first 100 events

[rapid escarp]

right so which 100 am i looking at?

do i pick the whole data then?

[winter torrent]

yes you'll need to use the whole data, but first you need to make that histogram

[rapid escarp]

i did make taht histogram

*that

[winter torrent]

where is it?

[rapid escarp]

do i sent that here?

okay wait i deleted it

i'll remake it

[winter torrent]

really you need the data from that histogram (event counts)

[rapid escarp]

This is the histogram

😭 kinda lost what i'm suppsoed to get from this

[winter torrent]

okay, how wide are the bins here?

[rapid escarp]

100

[winter torrent]

no

that's how many bins there are

[rapid escarp]

oh lmao

[winter torrent]

how many seconds does each one represent?

[rapid escarp]

u mean how far apart the x axis things are

[winter torrent]

ye

[rapid escarp]

0.5

[winter torrent]

0.5...

[rapid escarp]

what's that supposed to mean btw?

[winter torrent]

0.5 what

0.5 years?

[rapid escarp]

0.5 milliseconds (?)

Lol

[winter torrent]

there were 7000+ events in the first 0.5 ms?

[rapid escarp]

i'm lost myself

[winter torrent]

how did you make this graph

[rapid escarp]

the timestamps array has everything in ms

this was the timestamps array:

timestamps = []
for i in range(len(lines)):
    timestamps.append(int(lines[i].rstrip().split() [3]))

[winter torrent]

okay, so each of those bar lines represents the number of events in some time interval

[rapid escarp]

the plot is trivial cuz:

plt.hist(timestamps, bins = 100)
plt.show()```

[winter torrent]

oh hmm

okay so you didn't ever get the data out, that's annoying

[rapid escarp]

rightt

wait

honestly i still don't get what that histoggram is about

lmao

*histogram

the y axis is supposed to be the events?

[winter torrent]

yes

[rapid escarp]

and the x axis is time in ms?

[winter torrent]

ye

[rapid escarp]

but that doesn't make sense

[winter torrent]

oh looks like plt.hist returns the counts as an array

why not?

[rapid escarp]

0.5ms gives 800 events?

[winter torrent]

well yes, perhaps the bottom axis is not measuring in ms

[rapid escarp]

but we had this?

i think it might be in seconds

but how?

Lmao i don't have a single instance of "seconds" in my code

[winter torrent]

my that is a very pretty 1e8 at the bottom of your graph...

what do you suppose it means?

[rapid escarp]

no clue lol

😭

[winter torrent]

what's the range of your timestamps?

[rapid escarp]

hold on

[winter torrent]

like what's the maximum one

[rapid escarp]

,calc 318579019 - 609

[woven radish]

Result:

3.1857841e+8

[rapid escarp]

,w (318579019 - 609) milliseconds to seconds

[woven radish]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by nyxie9151

[rapid escarp]

yeah that's the range

[winter torrent]

yeah so you notice that those markings go up to just over 3.0

and it has the 1e8 at the bottom

[rapid escarp]

righttt

okay okay i see

so it is indeed in milliseconds

with a factor of 10^8

cool

now it makes sense at least

[winter torrent]

yeah

[rapid escarp]

so like yeah each interval is

5 * 10^7 ms

what is that supposed to mean?

[winter torrent]

so for the first interval, it looks like we had about 7300 events

,calc 7300 / (5e7/1000)

[woven radish]

Result:

0.146

[winter torrent]

so around 0.146 events per second

[rapid escarp]

wait

you're talking about this thing?

looks like it gets pretty close to 8k

unless you look at the starting thing only

[winter torrent]

specifically that first bar

[rapid escarp]

why?

[winter torrent]

well that's the first interval

[rapid escarp]

oh LOL

each line is 100 data points right?

cuz bins = 100?

[winter torrent]

each line is not 100 data points; there are 100 lines total

[rapid escarp]

oh so how many ever events/100

right and why did you choose the first line?

why not somewhere in the middle?

[winter torrent]

just as an example because it was easy to see

[rapid escarp]

okay

[winter torrent]

the next one looks like it's about 7400, so there are 7400 / 5e4 events per second in that interval

[rapid escarp]

so events/seconds -> 7300/(5e7/1000)

yeah i get that for the first thing

[winter torrent]

right

so then you'd do that for all 100

[rapid escarp]

am i supposed to do this in code?

[winter torrent]

yes :)

[rapid escarp]

how

😭

[winter torrent]

np.hist returns an array of those 100 values

i think

[rapid escarp]

dang

i'll search it

thankss

[winter torrent]

https://stackoverflow.com/questions/9141732/how-does-numpy-histogram-work

[rapid escarp]

yeah you're right

i think it's numpy.hist() indeed

[winter torrent]

[rapid escarp]

at least that's what it says here lol

lemme try

[rapid escarp]

idk 😭 if i'm actually messing things up but

is that how an array is parsed in numpy?

i don't see 100

[winter torrent]

hmm that looks like about 100 elements

but it also looks like you're getting two arrays back?

i think it's giving you the bin edges as well

[rapid escarp]

yeah i think so

[winter torrent]

the code they have is like hist, bin_edges = np.histogram(data, bins=100)

[rapid escarp]

oh i can seaprate

right yeah

okay thanks

[rapid escarp]

wait bin edges isn't the x value though right?

am i supposed to somehow extract the x value too?

[winter torrent]

bin edges is the x values but like... you don't really need them per se? they're equally spaced

if you want, you can use that second element [1] to get the bin width

[rapid escarp]

oh yeah they're 5e^7/1000 apart

each bin

[winter torrent]

looks like they're around 3e+06 apart to me

not sure where the 5 came from

[rapid escarp]

wait my bad

but hmm

3.18 * 10^8/1100

oh yeah it's 3.18 * 10^6

[winter torrent]

ye

[rapid escarp]

wait

,calc 7000/(3.18 * 10^6)

[woven radish]

Result:

0.0022012578616352

[rapid escarp]

i'm doing something wrong, aren't i

[rapid escarp]

wait so i do event/that for everything?

😭 no clue why it truncates to integer

even though every element in the array is float by default

[winter torrent]

those integers are counts

there were 7407 events in the first 3.186e+06 milliseconds

[rapid escarp]

indeed

i do the division and it truncates to 0 lol

[winter torrent]

what are you dividing?

[rapid escarp]

7407/3.186 * 10^6 for example

cuz they want events/second

[winter torrent]

looks like it works for me?

[rapid escarp]

plt.hist(timestamps, bins = 100)
hist, bin_edges = np.histogram(timestamps, bins=100)


for i in range(len(hist)):
    hist[i] = float(hist[i])/ (3.18 * pow(10,6))

print(hist)

[rapid escarp]

wha

I get these lol

[winter torrent]

oh

this is numpy trolling you

hist is going to be an array of dtype=int64

so it can only take integers

and it'll convert everything to an integer

[rapid escarp]

nooo i hate numpy

okay so i make a copy?

[winter torrent]

yes... but you'll need it to be a different dtype

or you can just do hist2 = [0.0] * 100

but that won't be a numpy array just a normal python list

[rapid escarp]

oh yeah i already made a copy

i don't need numpy array ig 😭

wait

i guess i do need numpy arrays cuz i have to do std and avg lmao

ughhh

[winter torrent]

https://www.geeksforgeeks.org/change-numpy-array-data-type/

[rapid escarp]

right i fixed it

apparently i just needed to do

hist_float = histastype(float)

[rapid escarp]

oh this says just that too

okay so i have like 0.01

so like 0.01 * 100 = 1%

thanks @winter torrent !

[winter torrent]

yay~

we got there

[rapid escarp]

eventually

just to confirm

😭 we do multiply by 100 right?

since the coefficient is a scalar

or it isn't normalized or smth?

[winter torrent]

multiply by 100% (which is 1)

[rapid escarp]

right but nobody uses it in percents right?

[winter torrent]

0.01 = 1%

[rapid escarp]

i was reading through wiki

[winter torrent]

oh do they not? i haven't really used CV much

guess that makes sense since it's a coefficient

[rapid escarp]

right i haven't either 😭

they just go okay it's 0.567

but hmm yeah fair enough

thanks for the help once again!

[rapid escarp]

wait LOL

they say "coefficient of variation"

but then they're saying percents on the answer choice

which is funny

[winter torrent]

yeah i mean

[rapid escarp]

cuz both answers are there

[winter torrent]

0.01 = 1% like those are the same thing

[rapid escarp]

literally doesn't make snese tbh

[winter torrent]

0.13 = 13%

etc

[rapid escarp]

no but the coefficient of variation is 0.01

without the percents

[winter torrent]

it's also 1%

with the percent

[rapid escarp]

they ask for the coefficient of variation

[winter torrent]

those are the same thing

it's not 0.01%

[rapid escarp]

but if they asked you for the coefficient of variation

then it's strictly 0.01 right?

without the %'s at all?

but yeah i get your logic i guess yeah

sorry 😭 i'm probably just being dumb

anyway

thanks

.close

[devout snow]

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[broken badge]

okay so I need help with this problem

[broken badge]

I actually think i understand it

but my professor is.. well... an ass

here is the problem: A random sample of size 100 is taken from a continuous exponential distribution. The sample mean is found to be 6.25. Construct an approximate 95% confidence interval for the true mean of the exponential distribution.

here is my work:

here is where it mentions the standard deviation being the same thing as the mean for an exponential distribution:

Its already been established in this class that sample standard deviation and mean are UNBIASED estimators for the population mean and STD

here is what my professor says:

[devout snow]

@broken badge Has your question been resolved?

[devout snow]

@broken badge Has your question been resolved?

[devout snow]

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[broken badge]

.reopen

[devout snow]

✅

[eager fox]

Well your solution lacks explanation

[broken badge]

i wrote a big ass arrow after the sample size of 100 stating i was using central limit theorem and therfore a normal dist.

I defined the formula for a confidence interval

stated that the sample standard deviation was an estimator for the mean and vice versa

[eager fox]

Did he want you to write in words why what u did worked?

[broken badge]

I have no idea,

No so not explicitly stated in the questionL

just asked: " A random sample of size 100 is taken from a continuous exponential distribution. The sample mean is found to be 6.25. Construct an approximate 95% confidence interval for the true mean of the exponential distribution.:

[eager fox]

What level of education does your teacher have?

[broken badge]

phd

[eager fox]

Phd in?

[broken badge]

applied mathematics ..

Im just so mad I feel like I did this exactly right and got the shaft bc they just decide to arbitrarily count off points

[eager fox]

He may just not even understand what he himself is teaching. He said u got the right answer but no explanation?

[broken badge]

He doesnt dude

[eager fox]

He said you have the correct interval

[broken badge]

The damn textbook uses answers in the back of the book based on a welsh t test when the book itself never metnions that

[eager fox]

Does he have office hours?

[broken badge]

he does but is never there

[eager fox]

U can ask and explain what you did to him

[broken badge]

and hes the department chair so he can get away w it

I will see if I can explain

I just dont understand why its not clear what I was doing

[eager fox]

Hes prob a schmuck

Just play to his ear and he'll like you

[broken badge]

thanks

.close

[devout snow]

Channel closed

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[devout snow]

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[icy viper]

A bullet was shot with a mass of 15 g at a speed of 2.8 m/s

[icy viper]

On a wooden plate that has a thickness of 5 cm

The bullet passed through the wooden plate losing 3/4 of its original speed

Find the value of the wooden plate resistance

Against the bullet

<@&286206848099549185>

Nvm I solved it

I thought the bullet was moving via force

But there was only resistance

The question now is ....

Why does the bullet not carry any force with it

And how do I know if there's no force affecting the object

<@&286206848099549185>

[inner bridge]

The object is moving freely

Without the effect of external force on it

That is the reason

You do not apply any force on it

[icy viper]

How do I know that it dosent have force applied next time I read a question

[devout snow]

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[calm seal]

Can someone help me with this? the question is to whether this is a function or not, but i don't know what those ''hollow points'' mean, and i have a very vague knowledge on limits

[desert flicker]

black dots indicate that it is the functional value at that point

hollow points indicate that it isnt

[calm seal]

So Y at the hollow point would mean that it is not functional at the X value?

[restive river]

observe it like this for a moment

the black dot means that the x value there is including

you're gonna get the same value of y for every x including the black dot

going on the middle one, now if we darken any of those dots, it will miean that at that value of x, function is gonna give us a y vaue

but since that value of x is already mapped

with some value of y

there would be no output, more like if we darken that dot, we are going to get to values of y for the same x

which is not possible

if it has to be a function

[calm seal]

Ah, i think i kind of understand it

i made a representation myself (im not quite sure if its accurate)

[restive river]

yea it is

the non darkened dots just simply means we are not taking that value of x

have y ever saw graph of greatest

integer

fraction?

[calm seal]

I dont think so

[calm seal]

So, if the white dots mean that it is not taking the value of X, it would still be considered a function, since now each X is outputting a single value of Y?

[restive river]

yes

[calm seal]

ooOoooooooo, now i think i understand

[restive river]

this graph means, if we put x $\in [0,1)$ we are gonna get the our answer = 0

[woven radish]

yajat

[restive river]

notice how

i havent used sqaure brakcets on one

it's because it has a blank dot

and then function is giving as value 1 if x$\in [1,2)$

[woven radish]

yajat

[restive river]

similary in this graph, for x$\in (-\infty,x_2]$ function is giving us a value $y^3$

[woven radish]

yajat

[restive river]

and for x$\in (x_2,x_1)$ we are getting $y=y^2$

[woven radish]

yajat

[restive river]

you get it now?

[calm seal]

Well, most definitely more than before

So the brackets are not used with hollow dots since they dont assign an x value?

[restive river]

i dont get your question

sorry

[calm seal]

Oh, i just wanted to know why the brackets are not used on hollow dots

I've seen the brackets usage before, but i dont really remember what they mean

[restive river]

ok so () mean that we are not taking the value of x and [] mean that we are

[calm seal]

Ah, yea that makes sense

[restive river]

read this if im noting sense

[calm seal]

Yea i think i get it

[restive river]

also you can watch a video on yt on greaatest integer fraction if you still feel like you're not geting it, the graph you sent before is pretty much the same

[calm seal]

Thanks for the help tho, test season is coming soon and i just needed to know this before going forward

[restive river]

ok

no problem, good luck for your exams

[calm seal]

Thanks 🙏

[restive river]

@calm seal .close to close the channel

[calm seal]

Oh, right

.close

[devout snow]

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[devout snow]

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[vivid estuary]

Need some clarification:

So I know that associativity says (ab)c = a(bc) and that it does't give us the right to do (ab)c = (ac)b, which separates it from commutativity. I had a question on commutativity though, so it says a + b + c = b + c + a, meaning the order does not matter in the way you list them from left to right but commutativity doesn't say the order in which we operate on the expression does not matter right? So saying (a + b) + c = b + (c + a) is commutativity would be wrong right

[vivid estuary]

So associativity allows us to say the order in which we operate on the expression does not matter and commutativity say the order in which we list the terms does not matter but one never implies the other?

[dusk jacinth]

Commutativity is ab = ba.

[dusk jacinth]

Are you looking for quasi-commutativity?

[vivid estuary]

I'm not sure what that is I'm just trying to make sure I understand commutativity and associativity right, does commutativity only apply for two variables?

[dusk jacinth]

does commutativity only apply for two variables
It only applies to operators of two operands (binary operators), yes

a + b = b + a.
Similary,
(a + b) + c = c + (a + b).

[vivid estuary]

ah ok I see

[dusk jacinth]

(amo)+(gus)=(gus)+(amo)

The law only involves one instance of the operator (in LHS and RHS)

In contrast,
associativity is (a+b)+c = a+(b+c), you have two instances of the operator

[vivid estuary]

oh ok that makes sense, and with associativity alone we can't do (a+b) + c = (a+c) + b right?

[dusk jacinth]

Exactly, we can't do it. We need at least quasi-commutativity for that.

[devout snow]

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[brave valley]

What i did wrong?

[brave valley]

Oh

I should have written 2

[solar goblet]

this channel gonna close soon so yall should prolly move to a new one

[restive river]

thanks fungus

[brave valley]

Why?

[restive river]

.

[restive river]

.

wdym why 😭

[brave valley]

?

[devout snow]

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[zinc raven]

i do not understand the BLUE

[acoustic leaf]

which part do you not understand?

[winter patrol]

they're apply the inverse relation between e and ln
and exponent/log laws to first simplify that component

[zinc raven]

what law-

also how did x^-4 go down from being an exponent

[solar goblet]

$e^{\ln x}=x$

[woven radish]

∮μ²ƞdS

[zinc raven]

oh so it's just the rule in its entirety-

aight thx

[zinc raven]

:D

[solar goblet]

!done

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[undone stump]

wondering if correct

[devout snow]

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[normal verge]

To determine whether the function ( f_1: \mathbb{Z} \rightarrow \mathbb{Z} ) given by ( f_1(z) = 3z - 1 ) is injective (one-to-one) or surjective (onto), let's examine the definitions and try to prove or disprove them.

1. Injectivity: A function is injective if each element of the domain is mapped to at most one element of the codomain. In other words, different input elements are mapped to different output elements.

To check injectivity of ( f_1 ), we assume ( f_1(x_1) = f_1(x_2) ) for two different ( x_1, x_2 ) in ( \mathbb{Z} ). Then we need to show that ( x_1 = x_2 ).

Assume ( f_1(x_1) = f_1(x_2) ):
[ 3x_1 - 1 = 3x_2 - 1 ]
[ 3x_1 = 3x_2 ]
[ x_1 = x_2 ]

Since ( x_1 = x_2 ), the function ( f_1 ) is injective.

2. Surjectivity: A function is surjective if every element in the codomain has at least one element in the domain that maps to it. In other words, the function reaches every element in the target set.

To check surjectivity of ( f_1 ), we need to show that for every ( y ) in ( \mathbb{Z} ), there exists an ( x ) in ( \mathbb{Z} ) such that ( f_1(x) = y ).

For ( f_1(x) = 3x - 1 ), we can observe that for every ( y ) in ( \mathbb{Z} ), there exists an ( x ) such that ( f_1(x) = y ). For example, choosing ( x = \frac{y + 1}{3} ), we get ( f_1(x) = 3 \cdot \frac{y + 1}{3} - 1 = y + 1 - 1 = y ).

Hence, the function ( f_1 ) is both injective and surjective.

[woven radish]

ABDEL

[normal verge]

is that correct???

[uncut crow]

you can't be out here posting chatgpt answers and asking people to verify it

[normal verge]

i got the same answer so i asked chatgpt to write it

[uncut crow]

using chatgpt and then verifying it is OK but make more of an effort than that

[rapid escarp]

[normal verge]

so i can easly post it

that's why

[uncut crow]

you should really post your own answer then lmao

[rapid escarp]

lol where’s your effort?

[normal verge]

i said i got the same answer

[uncut crow]

send what you did then

[normal verge]

it's in german wait

[uncut crow]

fwiw yes the chatgpt answer is (surprisingly) perfect oops no it's not

[uncut crow]

this looks different than the question chatgpt answered

[normal verge]

yeah yeah one second

[uncut crow]

looks like there was a part (a) and part (b)

[normal verge]

is that also correct

[uncut crow]

what did the question ask?

"is f_2 a bijection?"?

[normal verge]

if it's injective or surjective

[uncut crow]

o ok

for showing f_2 is not injective

you just need to show there are two different integers that map to the same thing

so like, yes ok but why does this make it not injective

[normal verge]

cause the same element point to different Elements

[uncut crow]

wdym

[normal verge]

i mean f(z1) points to z1 and z2 so it's not injective

[uncut crow]

ok sure, so your point is f(z_1) = f(-z_1) for any z_1

i would just write f_2(1) = f_2(-1)

that's all you need to do to show f_2 is not injective

[normal verge]

okay 👍

ha surjective is it correct

[uncut crow]

the idea is ok

but you just need to present one element of Z that nothing maps to

[normal verge]

okay so i should find example

[uncut crow]

yea, what you did here might help you find an example but you don't need to include that in the proof

[normal verge]

okay so for Z2 = 5 / Z1 = \sqrt{2 }

[uncut crow]

also if i can make a suggestion: 3z^2 >= 0 for any z, so 3z^2 - 1 >= -1

so nothing maps to, say, -2

[normal verge]

and \sqrt{ 2} it's not in Z

[normal verge]

hmm

[uncut crow]

yea that's also fine

[normal verge]

thank you so much🙏

[uncut crow]

this is sometimes an integer, sometimes not

so just explicitly give one that shows it's not always an integer

[normal verge]

yes

[normal verge]

i still not sure about the second proof

cause Z2 might be equal to decimal number

and that's not in Z

so it's not surjective right??

@uncut crow

[uncut crow]

yea it's not surjective

[normal verge]

Cause I just noticed that by doing this one

[uncut crow]

a simple way to see it's not surjective is that nothing maps to 0

[normal verge]

ooh okay nice tipp

[normal verge]

i just understand what you mean by that

[uncut crow]

i often just play around with the function a little bit to start to see if there are "bad examples" at first to show it's not surjective or not injective

and if not then i'll try to prove it's surjective or injective

like for f_1, i would notice 3z-1 is never a multiple of 3

so can't be 0

or any other multiple of 3

[normal verge]

o okay 👍

now coming to hard one

i'll try to solve it

[uncut crow]

ok

what is df here

definition?

[normal verge]

i don't know actually, i always ignore it cause doesn't do nothing

[normal verge]

yeah maybe

[uncut crow]

probably equal by definition

i don't have any better guesses

[normal verge]

just ignore it hahaha

[uncut crow]

weird they write definiert durch but also df if it means definition though lol

[normal verge]

hmm

i think the comma between (x*y , x/y ) means the multiplication !!

cause R x R-(0) -> R x R

[uncut crow]

the comma means (x*y , x/y ) is a pair

[normal verge]

okay

[uncut crow]

so for example, (1,2) maps to (1*2, 1/2)

[uncut crow]

f is actually not injective

[normal verge]

hmm

[uncut crow]

let's just take something simple

(1,1) maps to (1,1)

can you think of anything else that maps to (1,1)?

[normal verge]

no idea

2 and 1/2 but it's incorrect

[uncut crow]

we're looking for (x,y) that maps to (1,1), so you want xy = 1 and x/y = 1

x/y = 1 forces x = y

so you also need x^2 = 1 (from xy = 1 and x = y)

so x ought to be...?

[normal verge]

y

[uncut crow]

no; x^2 = 1 implies x = ?

[normal verge]

-1 or 1

[uncut crow]

yea

[normal verge]

okay

[uncut crow]

so now can you think of something that maps to (1,1)?

other than (1,1)

[normal verge]

it's -1 , -1

[uncut crow]

yep

[normal verge]

hahaha i'm so dumb

i didn't think about it

to prove it's surjective it's normal right

like that

like x/y and x*y are in R x R

so it's surjective @uncut crow

[uncut crow]

i don't see how this proves it's surjective

[normal verge]

hmm