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Old 04-09-2017, 04:21 AM   #9426
masque de Z
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
Originally Posted by 1989 View Post
Statistics problem that I cant figure out, should not be too tough for you guys...

X and Y are random variables. They are independent and their distribution is equal.

EV(X)=1
Var(X)=2
EV(Y)=1
Var(Y)=2

Z = X*Y

What is the variance of Z?

What formula do I use?

Thanks in advance.
This here being a homework educational value thread probably one must never miss the chance to expand on these things and we can all learn more that way;

For example try also these links with detailed analysis and generalizations

http://www.coe.utah.edu/~cs5960-02/l...s/Lecture2.pdf

http://stats.stackexchange.com/quest...ndom-variables

Look also in the related product entry in the general link

https://en.wikipedia.org/wiki/Variance



https://www.jstor.org/stable/2281592

and


if independent.

notice



https://en.wikipedia.org/wiki/Covariance

This is worthy too

http://www.stat.yale.edu/~pollard/Co...7/Variance.pdf



Additional value

http://www.math.uah.edu/stat/dist/Joint.html

https://en.wikipedia.org/wiki/Product_distribution
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Old 04-27-2017, 03:08 AM   #9427
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Re: The Official Math/Physics/Whatever Homework questions thread

(forgot password to main account, sorry if this is against the rules)

I have a stats problem, happy with any direction people can point me in. For context I've done intro mathematical stats so I know how to do easier functions of random variable questions (CDF method, transformation method, mgf method) but I'm lost here.

Question:

u and v are i.i.d sampled from the uniform distribution [0,1]

if s^2 = (2u-1)^2 + (2v-1)^2 < 1, then x is sampled from the standard normal distribution. Otherwise, x = (2u-1) * sqrt( -2log(s)/s)

My first thought was to try and use the cdf method and then glue them together in a pdf, I'm not getting very far. The other problem I have is that it seems to me that the conditions imposed on s (if the square is less than 1) imply that the 'otherwise' section would result in a negative log.
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Old 04-27-2017, 05:55 AM   #9428
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Re: The Official Math/Physics/Whatever Homework questions thread

Oh should have added: how is x distributed?

Anyway, remembered pw to this account
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Old 05-10-2017, 06:59 PM   #9429
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Re: The Official Math/Physics/Whatever Homework questions thread

Not homework but something I wanted to figure out & I'm a complete drooler so maybe you guys could help me out. I have five people processing returns from several (call it 100) different companies every day. The companies take a different amount of time to process so 15 units of company A might take the same amount of time to process as 40 units of company B. Having records of how much of each company everyone did each day how do I tease out who's outperforming & who is just consistently grabbing the companies that get be processed fast to juice their total numbers?
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Old 05-10-2017, 07:45 PM   #9430
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Re: The Official Math/Physics/Whatever Homework questions thread

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Originally Posted by springs View Post
Not homework but something I wanted to figure out & I'm a complete drooler so maybe you guys could help me out. I have five people processing returns from several (call it 100) different companies every day. The companies take a different amount of time to process so 15 units of company A might take the same amount of time to process as 40 units of company B. Having records of how much of each company everyone did each day how do I tease out who's outperforming & who is just consistently grabbing the companies that get be processed fast to juice their total numbers?
It seems that you should be able to get an average processing time by company from the data. And then you can benchmark against that.
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Old 05-13-2017, 09:11 AM   #9431
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Re: The Official Math/Physics/Whatever Homework questions thread

Factorisation:

I am having trouble breaking down this expression in the way that is wanted. I am asked to factorise an expression using the difference of two squares.

(squared = (s))

3x(s) - 27y(s) = ?

The answer is 3(x-3y)(x+3y)

I have tried a lot of different ways of re-expressing it but I can not get the maths to compute to that.
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Old 05-13-2017, 09:40 AM   #9432
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Re: The Official Math/Physics/Whatever Homework questions thread

Let's pull out a 3 first to get 3x^2-27y^2 = 3(x^2-9y^2)

Now, you hopefully know that (a-b)(a+b) = a^2-b^2. If you set a^2=x^2 and b^2=9y^2, I think that you can find some pairs of square roots to find what you need.
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Old 06-19-2017, 02:17 PM   #9433
Danny McBride
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Re: The Official Math/Physics/Whatever Homework questions thread

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Originally Posted by darthsidius View Post
(forgot password to main account, sorry if this is against the rules)

I have a stats problem, happy with any direction people can point me in. For context I've done intro mathematical stats so I know how to do easier functions of random variable questions (CDF method, transformation method, mgf method) but I'm lost here.

Question:

u and v are i.i.d sampled from the uniform distribution [0,1]

if s^2 = (2u-1)^2 + (2v-1)^2 < 1, then x is sampled from the standard normal distribution. Otherwise, x = (2u-1) * sqrt( -2log(s)/s)

My first thought was to try and use the cdf method and then glue them together in a pdf, I'm not getting very far. The other problem I have is that it seems to me that the conditions imposed on s (if the square is less than 1) imply that the 'otherwise' section would result in a negative log.
I think this is an ANOVA (analysis of variance) question. From what I can recall from my stat lecture 10 years ago.
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Old 07-20-2017, 10:54 PM   #9434
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Re: The Official Math/Physics/Whatever Homework questions thread

I'm taking a maths course this summer, and apparently my geometry is a lot worse than I thought. Can someone help me with this?

Draw a parallellogram ABCD. From A, draw the line AN perpendicular to CD and the line AM perpendicular to BC (N lies on the line CD, and M lies on the line BC). Show that MAN ~ ABC (not quite sure what this translates to, but that the triangles MAN and ABC are similar I think?)



Any help would be greatly appreciated, I'm feeling like an idiot here.
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Old 07-21-2017, 12:02 AM   #9435
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Re: The Official Math/Physics/Whatever Homework questions thread

Call ABC angle x.

ABC is the same angle as MAN. Triangles ABM and AND are similar right triangles (they have same angles NDA is ABM ie both 180-x.

Then DAB is 180-x, ABM is 180-x so BAM is x-90 and NAD also x-90.

So MAN angle is 180-x+x-90+x-90=x ie the same as ABC angle.

From right triangles above mentioned being similar you get AN/AD = AM/AB =AN/BC.

So you have two triangles that have one common angle and their sides that form that angle are proportional to the same corresponding sides of the other triangle (same ratio). So they have to be similar.

To show that, imagine drawing the 2 triangles (MAN and ABC) with common angle ABC and a line parallel to NM from a point that is AB/AM away from A (on AM extended direction line) as AM is from A (ie the point B lol). Then that line on the other side crosses to point C basically creating the identical to ABC triangle (imagine it crosses to C' and prove it has to be C because of similar triangle properties as the just created triangle is similar to MAN and you can prove AC=AC').

Last edited by masque de Z; 07-21-2017 at 12:16 AM.
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Old 07-21-2017, 11:43 PM   #9436
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Re: The Official Math/Physics/Whatever Homework questions thread

Thanks a lot masque, I really appreciate the help. Hopefully the rest will come easier to me, otherwise I might be back
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Old Yesterday, 01:52 PM   #9437
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Re: The Official Math/Physics/Whatever Homework questions thread

Trig problem, probably something silly I’m not getting that I just need spelled out for me:

“Find tan(17pi/12) using the addition identity of two special angles”

The correct answer is (sqrt(3) + 1) / (sqrt(3) – 1) but I get something slightly different:

When I do the problem I get:

Tan(17pi/12) = tan(9pi + 8pi/12) -> 3pi/4 + 2pi/3

Sin(3pi/4 + 2pi/3) = sin(3pi/4)cos(2pi/3) + cos(3pi/4)sin(2pi/3)

Cos(3pi/4 + 2pi/3) = cos(3pi/4)cos(2pi/3) – sin(3pi/4)sin(2pi/3)

... (sin(X + Y) * 1/(cosXcosY)) / (cos(X + Y) * 1/(cosXcosY)) …

= tan(3pi/4) + tan(2pi/3) / 1 – tan(3pi/4)tan(2pi/3)

= (-1 - sqrt(3)) / 1 + sqrt(3))

So for some reason I am getting the negative of the correct numerator and the conjugate of the correct denominator in my answer...
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Old Today, 12:44 AM   #9438
masque de Z
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Re: The Official Math/Physics/Whatever Homework questions thread

Quote:
Originally Posted by JCA88 View Post
Trig problem, probably something silly I’m not getting that I just need spelled out for me:

“Find tan(17pi/12) using the addition identity of two special angles”

The correct answer is (sqrt(3) + 1) / (sqrt(3) – 1) but I get something slightly different:

When I do the problem I get:

Tan(17pi/12) = tan(9pi + 8pi/12) -> 3pi/4 + 2pi/3

Sin(3pi/4 + 2pi/3) = sin(3pi/4)cos(2pi/3) + cos(3pi/4)sin(2pi/3)

Cos(3pi/4 + 2pi/3) = cos(3pi/4)cos(2pi/3) – sin(3pi/4)sin(2pi/3)

... (sin(X + Y) * 1/(cosXcosY)) / (cos(X + Y) * 1/(cosXcosY)) …

= tan(3pi/4) + tan(2pi/3) / 1 – tan(3pi/4)tan(2pi/3)

= (-1 - sqrt(3)) / 1 + sqrt(3))

So for some reason I am getting the negative of the correct numerator and the conjugate of the correct denominator in my answer...
That should be ;

tan(3pi/4) + tan(2pi/3) / 1 – tan(3pi/4)tan(2pi/3)

= (-1 - sqrt(3)) / (1 - sqrt(3)) (- - - three times = -)

which is (1+√3)/(√3-1) as wanted.
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