help-19

[fast ivy]

and for the other answer

800-722

78

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[bitter fiber]

im really confused, how does the tension changing do anyting

[loud birch]

It's because the tension in the cable will at some point overcome the friction and start moving the boat.

[bitter fiber]

but isnt the equation to find f max always the same (cos coefficient of friction and normal reaction are same)

[odd edge]

@bitter fiber Has your question been resolved?

[loud birch]

Well, yes. But they are not asking for the maximal frictional force - just the frictional force for particular choices of the tension.

Remember that the frictional force is a (in this case) horizontal force, similar to the force from the cable. So if the boat doesn't move, it means that the frictional force and the tension is the same.

So I would argue that as long as the tension is smaller than the maximal frictional force, then the frictional force is equal to the tension.

[bitter fiber]

so would u do like 5900-F=3/4 x 800g?

[loud birch]

Hm, where did gravity go?

Ah, I see it

No, I would calculate 3/4*800g and compare it to the given tensions. If it at any point is smaller than a given tension, then the boat is on the move.

If it is larger than a given tension, then the frictional force is equal to that tension.

[bitter fiber]

but its smaller that all the tensions (comes out as 5880)

@loud birch so is it just a pointless question?

[loud birch]

lol, that's a strange question then

So each of the given tensions overcome the static friction force.

When they ask for "What is the frictional force when the tension is:", it's hard to answer, when the boat is on the move.

As soon as the boat starts moving, the static friction force is no longer relevant - and they don't tell us about the dynamic coefficient of friction, which is the one needed for moving objects. And the dynamic coefficient of friction is usually somewhat smaller than the static one.

I wonder if they just messed up the question or what is going on here.

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[winged turret]

Hi, again me. on the right picture is exercise i have done and on the left is the solution in book, what did i did wrong

[cursive field]

that can be split as $3^{200}\cdot\left(\frac{1}{8}\right)^{200}$

[clever fjord]

ren

[cursive field]

which can then be written as $3^200 \cdot \ 8^{-200}$

oops

[winged turret]

hm

[cursive field]

ARGH

TEXIT

[winged turret]

just delete the message ah

[cursive field]

$3^{200}\cdot8^{-200}$

[clever fjord]

ren

[winged turret]

i see

so my way of soling isnt good or_

solving

[cursive field]

idk what that was but yea

then that can be further written as $3^{200}\cdot2^{-600}$

[clever fjord]

ren

[winged turret]

i see

thanks again

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[wary musk]

I don't understand how the -37/20 calculated where it from like 0 - 1.85?

[upbeat imp]

Can you give context on what this is

[wary musk]

Probability

[upbeat imp]

Ah sorry I can’t help

[wary musk]

Probability and distribution and find the mean

[honest quest]

It hard to read the paper. Lot of tables value etc

[wary musk]

The formula is fine but hell I don't understand the -37/20 under the x-m

I'm confused about that part

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[ashen lily]

whats secant PBC here

[ashen lily]

and tangent

pls help

[ashen lily]

ummm its my channel

[slow garnet]

why is (c)=-2

[frigid canopy]

!occupied

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[ashen lily]

man can someone help me

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[woeful rivet]

hai again

[woeful rivet]

how i do?

part B

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[amber gorge]

Can i ask a question about Machine Learning?

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[cold sage]

well?

any ideas?

[umbral stratus]

like first term

doubles

then subtract one

3*2 - 1 = 5

then

5*2 1 = 9

i got this part but

cant figure out the formula for this

like how can use gp sum on this

[cold sage]

do you know the generic form of an arithmetic term?

[umbral stratus]

yes

[cold sage]

what is it

[umbral stratus]

so ap sum is n/2(2a+(n-1)d)

[cold sage]

it is

[umbral stratus]

?

[cold sage]

yeah, literally just use that

though you need to find a and d, which can be done by observation

[umbral stratus]

$20/2 * ((23)+(19d)$

[clever fjord]

ds23

[umbral stratus]

cant figure out d though

[cold sage]

what do the terms increase by?

[umbral stratus]

2, 4,6,8

[cold sage]

ooh blimey, sorry my eyes must have gone wonky i somehow imagined it being a constant step of 2

[umbral stratus]

no worries

[cold sage]

2,4,8,16,32,...
these are the steps, they are a geometric progression
we can find the sum of said steps, then add 20
(note that the given sequence 3,5,9,17,... is just the above with each term having a +1)

so the terms look like An=1+2^n

[umbral stratus]

wow

got it

thanks a lot

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[mystic saffron]

Can somebody tell me where I went wrong

Bruh

lol

nvm

i realized

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[wooden swan]

what order of steps should i do to solve this

to show work

convert into yards? then take deceimal into feet?

then take decimal into inches?

or is there a better way

[mystic saffron]

yours sounds right. it wants you to go in the order of yards, feet, then in

[wooden swan]

@clever fjord

, 210*36

,210*36

bro

,help

[clever fjord]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[wooden swan]

,list

[clever fjord]

My commands!

Use ,ls to obtain a briefer listing, and use ,help <cmd>to view detailed help for a particular command, or ,help to view general help.

If you still have questions, talk to our friendly support team here.

LaTeX Rendering

Render LaTeX code and configure rendering options.
​ ​ ​ ​ ​ ​ ​ ​ ​ ​ tex: Render LaTeX code.
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Page 1/4

[wooden swan]

how do you just use it for math

[quasi sparrow]

#bots

[wooden swan]

how do i show my work for this? 210in* ( 1 * 360)=y

?

withouto spaces obv

[west merlin]

$210in\cdot(1\cdot360)=y$

[clever fjord]

Wumbo

[west merlin]

like this?

[wooden swan]

yeah

is that teh rightthing

if i add answer

[regal chasm]

https://latexeditor.lagrida.com/

[west merlin]

what

[wooden swan]

i meant is that the right way to show my work?

[regal chasm]

it's website to write easily equations in latex. spinier wanted to learn how to write equation in discord no?

[wooden swan]

well its helpful for the future but im just wonderinf if showed my work right

[west merlin]

i personally would've done something like, (210in/1)*(1yard/36in)=blank yards

take the whole number from that as yards, and convert the decimal to feet, repeat the process, then inches

[wooden swan]

would writing 210in*(1yard/36in)=blank Y be the same?

[west merlin]

yes

[wooden swan]

ok

[west merlin]

unit conversion is what you're working on i'm assuming

[wooden swan]

then i would do the same thing with the decimal

[wooden swan]

yeah i allready did it in another math course, but im doing it agai nand forgot how to show my work

i know how to do it without showing just quickly times or divide but yeah

[west merlin]

i believe so yeah. you take whatever the decimal is, which is currently in yards, and unit convert that into feet

and then do the same process with the decimal from feet for inches

comes out pretty cleanly i believe

[wooden swan]

so like .83yd*1f/12y=answer

[west merlin]

$\frac{0.83yd}{1}\cdot\frac{3ft}{1yd}$

[clever fjord]

Wumbo

[west merlin]

that way the yards cancel each other and you're left with ft

[wooden swan]

oh yeah nvm

[wooden swan]

2.49?

[west merlin]

i believe so yea

[wooden swan]

then ,49f*12/1=answer

so final answer "5YD 2F 5.88IN" ?

[west merlin]

yea, if you hadn't been rounding though it would've popped out as 5.9999, which at this point would just be 6

[wooden swan]

? i didnt round?

oh im stupid i donce

[west merlin]

yea first one would've been 5.8333333333...

rounding compounds errors quickly

[wooden swan]

normal we show 2 decimal places should i just write 5.99 or just 6

nvm

6 obv

[west merlin]

5.99 would be correct imo if you put that down

but 6 is probably what they want

[odd edge]

@wooden swan Has your question been resolved?

[wooden swan]

should i convert 3 miles to yards

then divide by 100 then times by 90

@west merlin

k nvm that question

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[river idol]

What are you guys getting for 8b

I am having a conflicting answer with answer key

[plain hinge]

what's the answer ?

[river idol]

25200

[plain hinge]

o

i forgot my permutations 💀 need to revise that

[river idol]

What are you getting

[odd edge]

@river idol Has your question been resolved?

[worldly zephyr]

oh wait 8 b

ok so we know we cant use the numbers 4 5 6 7

as first digits

or 0

thats the question

this should help a lot

the first numbers can only be 1,2,3

and number has to be odd

[river idol]

Oh wait I got it, I didn't realize the same odd number at the start can't be at the end too

Thanks tho

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[plain sun]

can someone please help with e(ii)

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[undone mauve]

do you know that 1 + w + w^2 = 0

[plain sun]

yea

[undone mauve]

so what could 1 - w - w^2 be?

[plain sun]

2

-(1+w+w^2) + 2

I have no idea for the next 2 though

[undone mauve]

well you could substitute values and stuff if you need, or just divide by omega so you get w^2 - 1 + w, same for the third bracket

[plain sun]

how do I substitute the values though

[undone mauve]

w = (-1 + root(3)*i)/2

[plain sun]

ohhhh shit yea

so the middle one is -2w

and the third is -2w^2

so multiplying it together we get 4w^3

which gives 4

and then you times 2

which is 8

[undone mauve]

ok

[plain sun]

is that correct

[odd edge]

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[tall wolf]

Idk how they simplified to that answer

[tall wolf]

like I understand the whole process

but

how did they simplify

[halcyon parrot]

which step

[runic swift]

2sin(x)cos(x) = sin(2x)

let x = 5x

[halcyon parrot]

that is an identity

[runic swift]

yep

[tall wolf]

I still don’t get it

Because

I understand it’s an identity

but when u solve the whole q

it’s = 2 sin (10x) x 5

[cursive field]

okay two questions:

1. is that WA?
2. they mean $\sin^25x$ right

[clever fjord]

ren

[tall wolf]

yea

[cursive field]

okay

wait yea to 1 or 2

[tall wolf]

2

[cursive field]

alr

anyway just integrate i think

[tall wolf]

No it’s just taking the derivative

when u do that

u get

= 2sin(5x) x 5cos(5x)

but

when u turn it into

A identity

[cursive field]

oh sorry

i thought they said $y' = \sin^25x$, mb

[clever fjord]

ren

[tall wolf]

It’s 5[ 2sin(5x) x cos (5x) ]

then

put into an identity

Is

5[ 2 sin (2(5x)) ]

which is

[runic swift]

when you changed into that identity, you remove the 2

[tall wolf]

u do ?

[runic swift]

yes

2sin(x)cos(x) = sin(2x)

[tall wolf]

Ohhhhh

[runic swift]

not 2sin(x)cos(x) = 2sin(2x)

[tall wolf]

😭😭😭💀💀💀💀

My badd

simple mistake

funny part is they give us a formula sheet

💀

Thank you

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[haughty blaze]

$$\text{Why is it if 2 vectors are linearly independent then}$$
$$q\textbf{a}+p\textbf{b}=m\textbf{a}+n\textbf{b}\Longrightarrow q=m,\ p=n$$

[clever fjord]

quan

[crisp wadi]

Try moving what's on the left hand side to the right hand side of the equation and factor, what do you get?

[haughty blaze]

(q-m)a+(n-p)b=0

ah so q=m and n=p by the definiton

[crisp wadi]

Yup

[haughty blaze]

Also, do u mind if u explain intuitively what linear dependence means to you?

Like how do u think of it

Bc I know the definition

But intuitively im not sure

[crisp wadi]

It's pretty much the same as saying that you don't have any "extra" vectors that could be written using other vectors in your set

[haughty blaze]

So basically for two vectors we want it so we form two lines that cross over if we input all possible scalars? - for linear independence

And then for a set of three vectors that are linearly indepnednet what would it look like once we input all the possible scalars?

[crisp wadi]

Yeah and if those two lines are distinct, then the vectors are linearly independent

That works only if you have two vectors though

If you had more, you shouldn't be looking at the lines but at the spans

[crisp wadi]

So linear independence for 3 vectors would mean that if you take any pair of vectors (v1, v2), then the third vector v3 will not be contained in the plane that crosses v1 and v2

[haughty blaze]

ohhhh

so two vectors coplanar then one vector isn't = a plane is formed

???

[crisp wadi]

Any two vectors are coplanar though

[haughty blaze]

Oh yeah

😭

Of course

scalar triple product = 0 then we know its linearly dependent?

[crisp wadi]

What do you mean by scalar triple vector?

[haughty blaze]

product sorry

[crisp wadi]

The determinant of the matrix with those vectors as columns?

[haughty blaze]

(a * b) x c

if a, b and c are vectors

[crisp wadi]

Ah yeah that's the same iirc

[haughty blaze]

Alright cool

So the idea is that if we have 2 linearly independent vectors = we form two lines that cross each other

We have 3 linearly indepnedent vectors = we form a plane

[crisp wadi]

That cross each other only once*

[crisp wadi]

Form planes for each pair of vectors, yeah

[haughty blaze]

Oh right, 3 planes are formed?

[crisp wadi]

Yeah you need to check that this holds for all pairs of vectors (v1, v2)

Just one isn't enough

Actually just one would be enough if v1 and v2 are linearly independent

Hold on I'll give an example

For example if we have {(1, 0, 0), (2, 0, 0), (0, 3, 0)}, then the plane crossing (1, 0, 0) and (2, 0, 0) does not contain (0, 3, 0)

But the set is still linearly dependent, meaning you should check other 2 planes too

And next you would see that the plane crossing (1, 0, 0) and (0, 3, 0) contains (2, 0, 0) and concluce that the set is linearly dependent

[haughty blaze]

oo i see

[crisp wadi]

But computationally I would imagine that using the scalar product is way more efficient than just checking these subspans

[haughty blaze]

is it correct tho that the span of linearly indepednent vectors forms 3 distinct planes tho? because that means non co-planar vectors we have possible equations in form r(a,b)=c+ta+sb where c,t and s are

vectors that are linearly independent

[crisp wadi]

Yeah, any 3-dimensional space contains 3 distinct 2-dimensional subspaces

[haughty blaze]

Sweet, thanks bro also is subspace is a synoynm for plane?

[crisp wadi]

2-dimensional (sub-)spaces = planes

[haughty blaze]

Thank u!

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[halcyon parrot]

How to prove that sin2x. = 2sinxcosx

[honest quest]

comes directly from trig addition/subtraction identities.

[odd edge]

@halcyon parrot Has your question been resolved?

[olive ledge]

$\sin(x + x) = \sin(x)\cos(x) + \cos(x)\sin(x) = 2\sin(x)\cos(x)$

[clever fjord]

ColdTee

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[tall wolf]

How do you determine the asymptotes without graphing for y = cos x

[odd edge]

Please don't occupy multiple help channels.

[mystic saffron]

i mean

start by checking vertical asymptotes

[tall wolf]

howww

[mystic saffron]

a preset for a vertical asymptote to exist is for that point to not exist in the function's domain

but, what is the domain of cos(x) do you think?

[tall wolf]

0 less then or equal to x less then 2 pi

that’s what the question says

[mystic saffron]

well is cos(x) undefined at all on that interval?

[tall wolf]

idk

wdym

[cursive field]

1/0 is undefined

is cos x ever undefined

like, unevaluable

[halcyon parrot]

do u know how to check for asymptotes

[odd edge]

@tall wolf Has your question been resolved?

[odd edge]

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[true gate]

So im a bit confused on something

[true gate]

When the line has close points on both sides is it increasing or decreasing or neither

[cold sage]

im not entirely sure what you mean

do you mean what is it doing at the points themselves?

[odd edge]

@true gate Has your question been resolved?

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[autumn wadi]

Why isnt following statement true?

[autumn wadi]

If the Taylor series of a function ( f : (-1, 1) \rightarrow \mathbb{R} ), which is differentiable arbitrarily many times, converges, then ( f ) can be represented on ( (-1, 1) ) by a power series.

[clever fjord]

TIMT

[odd edge]

@autumn wadi Has your question been resolved?

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[mystic saffron]

24

also use a calculator

?

[cursive field]

@iron veldt idt that's a question you can ask here

can you @mystic saffron ?

i mean idk it just doesnt seem like the thing we can help u with

sorry just wondering idm if u ask

it came out wrong

[mystic saffron]

Learn the multiplication table!

And don't ask questions like that here

[cursive field]

or literally add it up

[cursive field]

yep, thought so

its not even hard

if you need to ask for 8x3 ur probably too young for dc anyway

how old are you

@iron veldt ?

OH MY GOD

[mystic saffron]

I mean there is nothing strictly saying you cannot. It's just 1- people who post this are likely trolling 2- it is much more efficient to refer to other resources online because explaining such fundamental topics is hard over discord

[cursive field]

<@&268886789983436800>

[mystic saffron]

editing a ping won't actually ping them

<@&268886789983436800> OP said they were 8 but deleted it. Check the logs.

Oh wow

8?

Sure

[warped grove]

Well

You said you were

[cursive field]

that is much too old to use discord

[warped grove]

.close

[odd edge]

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[cursive field]

well there they go

[odd edge]

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[umbral bone]

I’ve been trying this question for ages and am not sure why my answer is wrong?

[umbral bone]

This is my answer btw but it’s wrong

I need to find the turning point of the equation in red

Oh the negative…

smh how could’ve I have…

Ty

I’ll try it out now

Sorry, just to make sure, could u circle the part u r talking abt?

Actually I think I’m fine

Hm I still got it wrong for some reason?

Can U find out why?

I can't seem to find where my calculations are wrong but it's late, I may just be tired

<@&286206848099549185>

[wind hemlock]

I don’t understand what question is this

[umbral bone]

The red on top is the question and I am trying to find the turning point of the parabola

[wind hemlock]

This one

[wind hemlock]

Same as -

You only need to multi 1/3 once

It is
y=(x-2/3)*(x+4)

[umbral bone]

Oh so I don't need to multiply both 1/3 to both brackets?

Only the first one

Hm then why is the whole thing divided by 3 then?

[wind hemlock]

You can multi either of them

[umbral bone]

Oh okay

But I still don't understand them why would the entire thing be divided by three in the fraction and not just one of them?

[umbral bone]

🙏 🙏 that makes so much sense now

Tysm for taking the time to write it out

I got the answer right ty

I think I'm done now ty again

.close

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[drifting edge]

X and Y are two independent Unif(0,1) random variables. Z=max{X,Y} is a new random variable which is the maximum of X and Y. What's the CDF F_X(x) of X for x in [0,1]?

[odd edge]

@drifting edge Has your question been resolved?

[drifting edge]

<@&286206848099549185>

[drifting edge]

F_X(x)= {
0 if x <= 0
x if 0 < x <= 1
1 if 1 < x
}

[toxic monolith]

correct, you've applied the general form properly

[toxic monolith]

but to be precise, such a formula, I require that must be also proven

[drifting edge]

We dont need to prove it for our class gladly

[drifting edge]

What is supp{Z}

because im confused idk why Z = max{X,Y} so it cannot vary

ohhh wait

[toxic monolith]

in simple words, informally , that is the set, where Z variable is defined, it should remind you the term :domain

[drifting edge]

because X and Y is vary

So then 0 -1

?

{0 <= Z <= 1}

[toxic monolith]

correct

[drifting edge]

For some z in supp(Z) what is P({X <= z} and {Y <= z}) in terms of their CDF ??

I think I know how to do it but idk how to multiply it with piecewise function

[toxic monolith]

if you have got CDF, or density, then yo can compoute that probability using them

[toxic monolith]

they are independent ones , and that gives you idea, how to calculate the intersecion of such events

[drifting edge]

F_X(x)= {
0 if x <= 0
x if 0 < x <= 1
1 if 1 < x
}

times itself except x = y on the second one?

[toxic monolith]

do not use sych sentence, it is not needed

[drifting edge]

wdym

[toxic monolith]

because, the variables are independent ones

[drifting edge]

It asked me to write the expression in terms of the CDFs F_X and F_Y, respectively.

Oh yes since they are independent I can just multiply their probabilities

But my question is how to multiply the piece wise function since it asks me to write in terms of the CDFS

[toxic monolith]

and now, you need to remind

the followjng concept,

what the relaiton between probability and CDF is

then

you translate

into CDF languge

[drifting edge]

CDF is the probability of it taking value less than the value

or equal to

[toxic monolith]

yes, though in my lectures, i suse sharp inequality

that depends on your isntructor

[drifting edge]

so basically it just P(X <= z) * P(Y <= z)

[toxic monolith]

yes

[drifting edge]

Ok now it asks me to write it as an integral

I think since its continuous then we can do that?

(0 to z dx) * (0 to z dy)

if 0 < z <= 1?

[toxic monolith]

exactly that is called: translation from CDF to PDF

PDF is base don integrals

aand CDF is deifned by INTEGRAL

[drifting edge]

It makes sense I think because it is less than or equal to

Ok now what is the relation betyween ({X <= z} and {Y <= z}) compared to {Z <= z}

[drifting edge]

???

Why -infty

it should start from 0?

[toxic monolith]

it is the defintion

and then when you write it, you next write

from zero

but you must always start with my formula

[drifting edge]

Ah ok

[drifting edge]

So I think ({X <= z} and {Y <= z}) means X and Y less than a random z in supp(Z)

[toxic monolith]

and there appears quesiotn it shud at you :

as you have noticed you were not usign Z variable right now at all

[drifting edge]

Yes now this is the confusion

[toxic monolith]

so the question, why your instructor

wud be ahppy

seeing

that you can also use thoery of Z

that is based on defintion of Z in yoru case

as maximum

so now

your main wrok

is:

to write = find the formula

for CDF or PDF

for Z variable

[drifting edge]

Yes haha

[toxic monolith]

then you can receive why it is important

[drifting edge]

The exact question

"How is the event {X <= z} and {Y <= z} related to the event {Z <= z}? Write down expression for CDF F_Z(z) i.e. F_Z(z)=P(Z <= z)

So I think ({X <= z} and {Y <= z}) means X and Y less than a random z in supp(Z)

And Z <= z means Z is less than a random z in supp(Z)

[toxic monolith]

ye syes so i did not see it but i felt it at once )

[drifting edge]

But is so abstract

Confused kinda

and how can Z test with z

it is itself no?

[toxic monolith]

it only requires of memorzing to do it once

thensuch proecss , regardlessly disitrubution , wil look the same

CDF of Z, you have to builkd on X and Y

ina following way

:

[drifting edge]

I know that Z = max{X,Y}

[toxic monolith]

yes i write latex, minute plz

and because , the both X and y are on [0,1] so finally you can write as second power of oen of them

i mayeb write fo royu general formula fo rn vairabels too

:

[drifting edge]

Smart to replace Z=max(X,Y)

Oh wait shoot

So they're basically the same thing

[toxic monolith]

of course all X+i are i.d.d

independent random vairables

[drifting edge]

this multiply?

[toxic monolith]

intersecion on sets =events

[drifting edge]

is like summation but multiply reight

[toxic monolith]

yes intersection

product is on numbers, interseciton is on sets

[drifting edge]

so basically the probability that all the variasbles are less than or equal to Z at the same time

[toxic monolith]

n your case = yoru assumption right

[drifting edge]

z*

[toxic monolith]

but due to applications

they rather shud be defined on same interval

applications of such processes decide

for example

you measure length

of some detail, metal one

or whatever

and you take sample

n detaikls

so you must use X_i on same interval

like

0,1

or wahter but the same

for all

your problem is such a base of thoeretiacl thigns fo rfuture to us eit in statistics

thoery of estimaiton

[drifting edge]

The few moments in which theory comes to existence haha

[toxic monolith]

smiles yes

[drifting edge]

What is PDF of the same thing?

I know it's F_X(z)*F_Y(z)

As CDF

But then do I have to convert it to integral

[toxic monolith]

if you ve got now, CDF of Z, then you can diffeerentiate it

o get PDF

right ?

[drifting edge]

Not sure

Oh yeah

[toxic monolith]

here was cdf of z

[drifting edge]

It is in my notes

[toxic monolith]

now take derivaite

derivative

and you get pdf of Z

[drifting edge]

hm then which variable to derivate

Since I have two

F_X(z)*F_Y(z)

[toxic monolith]

but look on photo

last thing

[drifting edge]

Oh do I just do d/dz

[toxic monolith]

right

[drifting edge]

Yeah the _X and _Y confused me

So basically just focus on the f(z)

[toxic monolith]

yes

[drifting edge]

so then final ans is d/dz(F_X(z)*F_Y(z))

[toxic monolith]

let me write it fo royu, to avoid eventual surprises ) 2 mins please

[toxic monolith]

in your case, n = 2

a= 0, b =1

that is CDF of Z

and now i also write the PDF

:

in notation, i used "characteristic function of the set", means 1 on [a,b] and 0 on the rest

so now, you have more general situaiton )

you can show you rinstructor )

i hope, that calculas i did in my mind, is obvious for you too

[drifting edge]

Ok i think it makes sense

I never saw that 1 thro

1_[a,b]

[toxic monolith]

you wil., especially

[drifting edge]

But it makes sense cuz thats the space for probability

[toxic monolith]

in theoetical topci like Proabibility base don theory of Measure

depends on yoru faculty

[drifting edge]

What's an example of a PDF f_X(x) whose associated continuous random variable X has expected value 10

E(X)=10

So I have the formula for E(X) for continuous

It is integral from -inf to +inf of x * f_X(x)dx

[toxic monolith]

if we stil talk about

uni distribution

then

E(X) = (a+b) / 2

so

if you set a = 0

then b = 20

and you get E(X) = 10

[drifting edge]

not sure if its uni or not tbh

the exact problem doesnt mention

[toxic monolith]

but we have to assume soemthing )

i supoose uni

but w can discuss Poisson

or

expoential one

etc

jsut you need formulaes

for

apporpaite EXPectation value

if we tlak about Poisson

then

EX) = lambda

0

[drifting edge]

Exact question:
Give an example of a probability density function f_X(x) whose associated continuous random variable X has expected value 10, i.e., E(X) = 10.

[toxic monolith]

so i gave you

th eeasiest one is uni

X on [0,20]

f(x) = 1/20

and zero on the rest

do you know hwo to fidn E(X) = a+b /2 ?

[drifting edge]

ohh wait so u r saying that it is asking us to choose

[toxic monolith]

or you re not interested

[drifting edge]

not interested xD

[toxic monolith]

smiles

pity haha

[drifting edge]

to choose whichever continuous

we want

since it didnt give us specific

[toxic monolith]

so uni helds your assumption

si continuouls

expoential oen too

then EX = 1/lambda

nice imporper integrals there :))

can ben also famous normal distribution as well where m = 10

then E(X) = 10 too

brb

[toxic monolith]

back

[drifting edge]

given this
Let X_1, X_2, ..., X_n ~ iid Ber(p) what is the sampling distribution of n * x̄ (capital X)

Bernoulli

iid=independent and identically distributed

[toxic monolith]

your questions have been written in some random way ? lol

to find it, i would start with Characteristic function of the random variable

in some way, if you deepen into , then it is just only mathematical analysis, that is what i love

[drifting edge]

probability distribution=sampling distribution?

[toxic monolith]

yes, the word is used to show you can use it in investigation fo distriution coming into consideraiton of populations, statistical ones and you discuss paramters if it comes to taken samples

from all populations

but theoretically

they are just random vairables

Mean, or Variance

mo slty

you wrote above the emprical variance

in the form

of unbiased estimator

due to presence of the denominator of the form n - 1

if you write n

then such esitmator is biased

it is Mathematical statistics

and to be precise : Theory of the estimation

point one .

you should start with :

[drifting edge]

it seems like n*X bar cancels out to X1+X2+...+Xn

do i start w supp(X1+X2+...+Xn)

but then many possibilities

[toxic monolith]

for every i = 1, 2, ..., n

n=1

since bernouli si special case of Binomial

distrubition

then we know that:

hence

the characiteristic function of the sum

is equal to product of such charactieristic functions means:

then finally we get:

we also write here that:

i used it above

[toxic monolith]

I go to rest, smiles thx for convo and the advantage of writing such nice things 🙂 smiles, Good Luck!

[drifting edge]

Ouch this looks hard

LOL

But thanks for giving me starting point!

[odd edge]

@drifting edge Has your question been resolved?

[odd edge]

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[tropic cargo]

what did I do wrong with my tabular integration?

[tropic cargo]

left is tabular right is regular integration by parts

<@&286206848099549185>

[quasi sparrow]

,w int 1 to 2 of (log(x))^2dx

[clever fjord]

Results provided by WolframAlpha

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

Requested by rie.mann

[quasi sparrow]

,calc 2log(2)^2 -4log(2)+2

[clever fjord]

Result:

0.18831730559662

[tropic cargo]

.close

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[devout trench]

Me and my friends have no idea what to do here. The graph comes out with 2 flat out x values, and ??

[ember oak]

The function is a parabola, so you you probably want an x interval that shows where the zeros intersect t x axis (assuming that they do), and you probably want a y interval that shows the peak of the parabola and also shows the y axis.

Your y interval is kind of wild because a computer can't display -infinity to infinity.

[devout trench]

The system says it can't have infinites :(

Since it's a window thingy

[odd edge]

@devout trench Has your question been resolved?

[odd edge]

@devout trench Has your question been resolved?

[odd edge]

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[granite schooner]

<@&286206848099549185>

[granite schooner]

hi

[gilded vector]

ask your question, wait 15 mins, then ping helpers

[granite schooner]

finaly someone

ohh

[gilded vector]

dont immediately ping

[granite schooner]

ok

okay

[gilded vector]

ok anyways what’s the problem

[ember oak]

!15m

[odd edge]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[ember oak]

(For extra context)

[granite schooner]

i have calc1 next semester and know 0 about math i know i could understand it but don't know where to start how to start what to start with nothing i know simple integral calc highschool level some other stuff but other than that i know nothing and even in the things that i named that i know so little about wdid?

i really need help

[ember oak]

If you know some integral calculus, you should be fine

Just review it

[granite schooner]

i sucked at at i hardly passed

and now i forgot all of it

don't know where to start how to start what to start with ,

can you help me with this ?

Rate Of Change
First Derivative
Derivative Rules
Extreme Values
Indefinite Integral
Definite Integral
Chapter Exercises
Matrix
Matrix Operations
Matrix Multiplication
Matrix Inverse
Cramer's Rule
Chapter Exercises
Exponent Equations
Logarithmic Equations
Series
Arithmetic Series
Geometric Series
Chapter Exercises

thats all i took and i forgot all of it

[ember oak]

Khan Academy would be a good source to review

[granite schooner]

what is that

let me google it

1 min

i see

wow this website looks good

i will see if i can use it i looked they have precalc and calc and i saw glimps of a video hope its good

thank you so much for helping

[odd edge]

@granite schooner Has your question been resolved?

[odd edge]

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[fallen prism]

,rotate 270

[fallen prism]

for the piecewise

num 1

a=2

so i subbed

25+5b-2=11

[pastel dew]

hey ei!

[fallen prism]

is this correct

[fallen prism]

hiii

[pastel dew]

yes it is

[fallen prism]

so b

is 13/5

?

wait no

-13/5

?

[fallen prism]

no -12/5

help

im so confused

[pastel dew]

this is right

[fallen prism]

23+5b=11

11-23=-12

-12/5

=b

[fallen prism]

okk

[pastel dew]

gg

[fallen prism]

i duno why this website said b=-3

[pastel dew]

[fallen prism]

its -12/5

[fallen prism]

okay tyysmm :DD

.close

[odd edge]

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[heavy knoll]

can someone help me with this one?

[glacial hound]

i feel like this is in the wrong server lol

[gaunt lynx]

hahaha lmoa

[heavy knoll]

its a chemistry question but it involves math aint it

[dense sonnet]

requires chem knowledge to get the math equation

[glacial hound]

exactly

[heavy knoll]

but it has math

get it get it

[dense sonnet]

hmm

[odd edge]

@heavy knoll Has your question been resolved?

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[tropic nest]

how to do the induction here

[tropic nest]

Kinda stuck here

[odd edge]

@tropic nest Has your question been resolved?

[odd edge]

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[magic quail]

do i plug in x+h for the second x? or just where its 3(x)^2

[mint mirage]

Everywhere

Because f(x + h) means plug in (x + h) for every instance of x

[magic quail]

ok thanks

so it should look like this?

for now

over h

[odd edge]

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[stiff yarrow]

Where do I begin?

[silver cobalt]

U say Hello

[cold sage]

hm

[stiff yarrow]

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[cold sage]

@stiff yarrow sorry, managed to figure it out

i see what i was doing wrong

so, if we have 8 heads, theres only 1 way that can happen, just 1/2^8
if we have 7 heads, there are 8 ways that can happen so 8(1/2^7 * 1/2)
if we have 6 there are 8!/(6!*2!)=28 ways, so 28(1/2^6 * 1/2^2)
in total we have 28/2^8+8/2^8+1/2^8=37/256

statistics isnt really my area so it took a bit

mainly the permutation part

[stiff yarrow]

thx

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[kindred frost]

true or false question, I learned how to solve stuff using the NPV formula but never learned about XNPV, so am unsure where go from here.

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[kindred frost]

😦

@cold sage sorry I saw u active can you help me?

[cold sage]

sorry, im not really familiar with the terms XNPV or NPV

[kindred frost]

net present value

[cold sage]

it looks like youre using excel? I assume it lists the inputs, perhaps just put in what you know

[kindred frost]

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[scenic vessel]

How do u add or minus functions that are abs and non abs

[scenic vessel]

,rotate

[river wadi]

Open mod f(x) like x²-1 would be positive in [1,infinity) so its abs will be also x²-1 now just add simply

But in [-1,1] x²-1 would be negative so its abs would be -(x²-1) which is 1-x²

[river wadi]

Since mod gives positive outputs you just do the negative of f(x) if its negative in that interval

Now just simply add f(x) +mod f(x)

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[outer wadi]

Is it just going to be a hemisphere?

[outer wadi]

But wouldn’t this make 2 hemisphere overlapped?

I’m having trouble with this problem it doesn’t make sense to me to revolve this around the y axis

I did the same question for revolved around the x axis and got 36pi but this one doesn’t make sense to me

I should probably rewrite the equation solved for x first

So I solved for x and got this shape but when I have solved for x in other problems the graph looked the same as when it was solved for y. Why does this one look different?

When I solve for x I’m taking the inverse of y right?

[brittle beacon]

Well for one, the function you have isn’t strictly invertible

And you also want to kinda like split it into two parts, and restrict the “inverse” domain

[brittle beacon]

If you add the restriction for this one (put {y >= 0} next to the equation) you’ll see it represents (the left) half of the semicircle you have

[outer wadi]

Why must be restrict the domain?

Oh is it because the original function did not have any negative y values

[brittle beacon]

Yep basically that

[outer wadi]

I think I got my answer, (45/2)pi, but shouldn’t I be getting half of what I got for the volume of the sphere which was 36pi?

So shouldn’t my answer be 18pi or is that not how it works

Yeah I checked my answer with the volume equation of a hemisphere and it’s 18pi, gonna double check my work

Found my error

Thanks for the help!

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[shut turtle]

Does ln k grows faster than k?

[river wadi]

till k=1 it does after that k has more slope

K has a constant slope 1

[shut turtle]

So it will converge?

[stark heart]

I think the way to find out is to find the points of intersection between ln(k) and k
Which has no points of intersection, which means that either k or ln(k) is always bigger
In that case k is always bigger than ln(k), which means as k goes to infinity the a_k coverages to zero

But that doesn't mean that the whole sum will converge

To test if the function will converge or diverge just use other tests than the a_n test

[shut turtle]

The answer is diverge

[stark heart]

The only test you can apply after the fail of convergence test (which is checking the limit of a_k as k goes to infinity if it is ≠0 then it diverges, if it is equal to 0 then the test fail) is using the ratio test which taking the limit as k goes to infinity fro the value (a_{k+1})/{a_k} if the result is between 1 and -1 then it converges if not then it diverges except for the value of 1 and -1 then the test failed

Do you know these tests or not?

[slow sandal]

consider the sum of 1/k from k = 1 to infinity

[shut turtle]

I just know it diverges because of the sum of 1/k as k—-> infinity is diverges

[shut turtle]

Yeah

[slow sandal]

obviously your sum is greater than 1/k

and the sum of 1/k diverges

[shut turtle]

Indeed

[slow sandal]

k grows faster than ln(k) also

[stark heart]

Yes

But knowing how to check for divergence or convergence using the 3 tests is also important.
Rather than relaying on your sense

[slow sandal]

comparison is valid

[shut turtle]

Yeah thanks

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[deep prawn]

Hello

I managed to simplify via polynomial division

but is there another way to do

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[keen light]

Question 10th

[keen light]

<@&286206848099549185>

.clise

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[tired crystal]

hi i don't understand how this is a function

[tired crystal]

so the domain is all real numbers mapped onto the codomain which is only the positive real numbers union 0

So if the domain is all of the real numbers then wouldn't that mean all the negative numbers of the domain would not have a co-domain to map onto

[pastel dew]

te negative numbers do map to positive numbers

[pastel dew]

is it written with smokes ?

[tired crystal]

sorry i don't know what you mean?

smokes?

[pastel dew]

nvm

[tired crystal]

but how do the negative numbers map to the positive ones? sorry could u explain

[pastel dew]

are you ok with that : $(-1)^2=-1(-1)=1$