thequickandthedead
Member
I know it looks like that but when you expand, simplify and factorize the original you do actually get that.
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The Math Help Thread
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cpp_is_king
Member
You won't have a constant term added to it. You already have the limits of integration for both variables. Integrate over one of those variables and apply the appropriate limits, and the constant term will vanish
But then -(2(αβ+αγ+βα
) has to be equal to zero. The unnecessary parentheses in the expression ((α+β+γ^2)-(2(αβ+αγ+βα) lead me to believe that an exponent or something is missing.How will it vanish, in this case? I suppose I am missing the "apply the appropriate limits" part, since after integration over b it would become (a/6) + 9/12.
Thanks for clearing this up.
cpp_is_king
Member
Yea, you're right, I didn't actually look at the function
Either way, I think it's fine to have that constant termYes, you're right about the dependence and independence.
Are you supposed to prove this? It almost reads like a definition. If e is the identity of G, then eH is obviously the identity of G/H due to the way multiplication in G/H is defined. But eH = {eh | h in H} = H. Or you could say that the identity of G/H is the unique coset containing the identity element of G, but H is a coset of H and H contains the identity of G, so H must be the identity of G/H.
Thank you, that helps.
Math sucks
anyways, working on some statistics homework super quick and I have absolutely no idea what I'm supposed to write.
Horse Racing. In a horse race, the odds against winning are as shown in the following table.
Horse/odds 1/8 2/15 3/2 4/3 5/30 6/5 7/10 8/5
A= event one of the top two favorites (the top two favorites are the two horses with the lowest odds against winning).
B= Event the winning horse's # is above 5
any ideas?
anyways, working on some statistics homework super quick and I have absolutely no idea what I'm supposed to write.
Horse Racing. In a horse race, the odds against winning are as shown in the following table.
Horse/odds 1/8 2/15 3/2 4/3 5/30 6/5 7/10 8/5
A= event one of the top two favorites (the top two favorites are the two horses with the lowest odds against winning).
B= Event the winning horse's # is above 5
any ideas?
Partial Gamification
Banned
I don't understand horse-racing odds, not a gambler, so it is weird to me that the odds there being a winner don't add up to one. Maybe its for ties and not finishing the race, other things that present each horses' chance of winning-and-losing as an independent event.
Prob(Win) = 1- Prob(Loss)
Prob(Win_MrEd): the probability Mr. Ed will win the race.
I did this and I guesstimate that the values make sense, but that doesn't mean its right:
I might have been reading your odds wrong too: % ?
How many '1' does the number 2^18564 has in binary notation?
It has one "1", located at the front followed by a ton of zeroes.
cpp_is_king
Member
Err. There's no question here, just a table with some odds.
cpp_is_king
Member
"Odds against winning" and "odds in favour of winning", when talking about gambling, is not the same as "probability of losing" and "probability of winning", respectively.
In gambling parlance, "odds against winning" is typically defined as (Probability of Losing) / (Probability of Winning) and the "odds in favor of winning" is the reciprocal of that.
This is done for some reasons related to how bookmakers compute payouts which I don't know all the details of.
Partial Gamification
Banned
I see, that makes it easy. Looking into the odds, there is Parimutuel betting, where the payout is determined when betting closes, as the odds had changed according to what bets were made. Its players are betting against themselves and the house generally keeps around 17% of the betting-pool.
The way the data is presented is confusing. I'm guessing horse/odds implies 1/8 means horse one has 8:1 odds against winning, horse two has 15:1 odds against winning, etc.
Wouldn't the most favored horses be the ones most likely to win for scenario A? I.e. the odds against winning for horse 3 is 2:1, so the odds for winning are 1:2, which in fractional for is a 1/3 chance of winning.
A) Chances either horse with the lowest odds against winning wins: the two lowest odds against winning are 2:1 (horse three) and 3:1 (horse four). The odds for winning are 1:2 and 1:3, or 1/3 and 1/4.
(1/3) + (1/4) = 7/12 chance either of the best two horses will win.
B) Chances any horse with number above 5 wins: The odds against winning are 5:1, 10:1, and 5:1 for those three horses, so the odds for winning are 1:5, 1:10, and 1:5. In fractions it's 1/6, 1/11 and 1/6.
(1/6) + (1/11) + (1/6) = 14/33 chance either horse 6, 7, or 8 will win.
Adding up all the fractional chances a horse will win gives 1.21. The excess is profit kept by the house, so .21/1.21 = ~17%, which is consistent with actual horse races.
LightOfTruth
Member
Edit: Emailed the professor and I did it fine. Book was wrong.
I need help with a Laplace Transform. Been a while since I've done them so I'm confused with how to do ones that aren't straight from a table.
f(t) = e^(-at)*sin(wt)*u(t-1)
I tried putting it into an integral form
F(s) = 0 - infinity integral e^(-at)*sin(wt)*u(t-1)*e^(-st)dt. I think it simplifies to this integral
F(s) = 1 - infinity integral e^t(-s-a)*sin(wt)*dt
Is this on the right track? I could of sworn there were patterns we learned to skip doing the actual integration but it;s been a while.
f(t) = e^(-at)*sin(wt)*u(t-1)
I tried putting it into an integral form
F(s) = 0 - infinity integral e^(-at)*sin(wt)*u(t-1)*e^(-st)dt. I think it simplifies to this integral
F(s) = 1 - infinity integral e^t(-s-a)*sin(wt)*dt
Is this on the right track? I could of sworn there were patterns we learned to skip doing the actual integration but it;s been a while.
https://docs.google.com/file/d/0B4twolbRFZCublpEYTlNWjVWQ2M/edit
Can anyone start me off on how they get from (13) to (15)? I understand the poles in the infinite semi circle part but not how the integration is done. Particularly unsure how the c^(q) fraction turns to 1/(rho^2*(dc^(q)/dq))
Can anyone start me off on how they get from (13) to (15)? I understand the poles in the infinite semi circle part but not how the integration is done. Particularly unsure how the c^(q) fraction turns to 1/(rho^2*(dc^(q)/dq))
Orbis Tabula
Member
Hey, can anyone help me with some simple questions regarding permutations, cycles, transpositions and all that? I did some homework, so I know the correct answers to my problems, but I'm curious if they're the only answers, since I'm not quite grasping this.
1. Let's say I have a permutation given by
(1 2 3 4 5 6)
(5 1 3 6 2 4)
And I'm told to find all orbits.
I know that
(1 5 2)(4 6) is correct.
Is (1 2 5)(4 6) also correct, or does order matter in this case?
2. Similar problem about not knowing if order matters. This time I need to break
(1 2 3 4 5 6 7 8)
(3 1 4 7 2 5 8 6)
into a product of transpositions.
I did this:
(1,2)(1,5)(1,6)(1,8)(1,7)(1,4)(1,3)
Could I reorder those, or is that the only correct answer?
Thanks for the help guys.
1. Let's say I have a permutation given by
(1 2 3 4 5 6)
(5 1 3 6 2 4)
And I'm told to find all orbits.
I know that
(1 5 2)(4 6) is correct.
Is (1 2 5)(4 6) also correct, or does order matter in this case?
2. Similar problem about not knowing if order matters. This time I need to break
(1 2 3 4 5 6 7 8)
(3 1 4 7 2 5 8 6)
into a product of transpositions.
I did this:
(1,2)(1,5)(1,6)(1,8)(1,7)(1,4)(1,3)
Could I reorder those, or is that the only correct answer?
Thanks for the help guys.
No, (1 2 5) means 1 goes to 2 goes to 5 goes to 1. The permuation you're given has 1 going to 5 and 5 going to 2 and 2 going to 1, not the other way around.
That isn't the only correct answer (you could also do (6,5)(5,2)(2, 1)(1, 3)(3, 4)(4, 7)(7, 8), or one of a billion other ways of doing it), but doing the same cycles in a different order won't work because cycles don't generally commute with each other if they're not disjoint.
Orbis Tabula
Member
Alright, thanks a lot for the help. Those were both pretty much what I was thinking, but I was afraid there was something I might be overlooking because my book was pretty short for this chapter. Thanks again.
Could someone help with this Gaussian Elimination question? I have no idea where I'm going wrong.
2x + 3y+ 2z = 35
x + y + 2z = 18
2x + 5y + 4z = 25
These are the steps I took:
R1 <--> R2
-2xR1 + R2
-2xR1 + R3
R2 <---> R3
-R2 + R3
R3 x -1/2
Which gives me a matrix of
x + y + 2z= 18
y = 3 2/3
z = 2 1/3
Which gives me x = 12, y = 3 2/3 and z = 2 1/3
I really don't know what I'm doing wrong.
Here's my working:
If someone could help that would be fantastic. Thanks.
2x + 3y+ 2z = 35
x + y + 2z = 18
2x + 5y + 4z = 25
These are the steps I took:
R1 <--> R2
-2xR1 + R2
-2xR1 + R3
R2 <---> R3
-R2 + R3
R3 x -1/2
Which gives me a matrix of
x + y + 2z= 18
y = 3 2/3
z = 2 1/3
Which gives me x = 12, y = 3 2/3 and z = 2 1/3
I really don't know what I'm doing wrong.
Here's my working:
If someone could help that would be fantastic. Thanks.
thequickandthedead
Member
But then -(2(αβ+αγ+βα
Sorry for the late reply but let me demonstrate why -(2(αβ+αγ+βα
) isn't zero.i get my values of α+β+γ and αβ+αγ+βα from the original equation (-b/a and c/a).
The question is Find the value of α^2+β^2+γ^2. (which is the same as (α+β+γ
^2)This simplifies to β^2-γβ+γ^2+γ^2-αγ+α^2+α^2-βα+β^2.
Which simplifies to (2(α+β+γ
^2)-(2(αβ+αγ+βα) (yes, i missed a 2 out)Then i just substitute my values of α+β+γ and αβ+αγ+βα into the final expression to solve the whole thing.
Sorry for the late reply but let me demonstrate why -(2(αβ+αγ+βα
i get my values of α+β+γ and αβ+αγ+βα from the original equation (-b/a and c/a).
The question is Find the value of α^2+β^2+γ^2. (which is the same as (α+β+γ
This simplifies to β^2-γβ+γ^2+γ^2-αγ+α^2+α^2-βα+β^2.
Which simplifies to (2(α+β+γ
Then i just substitute my values of α+β+γ and αβ+αγ+βα into the final expression to solve the whole thing.
That 2 was sort of a vital bit.
The bolded part is not very nice notation. Typically they are not the same.Sorry for the late reply but let me demonstrate why -(2(αβ+αγ+βα
i get my values of α+β+γ and αβ+αγ+βα from the original equation (-b/a and c/a).
The question is Find the value of α^2+β^2+γ^2. (which is the same as (α+β+γ
This simplifies to β^2-γβ+γ^2+γ^2-αγ+α^2+α^2-βα+β^2.
Which simplifies to (2(α+β+γ
Then i just substitute my values of α+β+γ and αβ+αγ+βα into the final expression to solve the whole thing.
I'm a bit confused by this. Did you verify thatSorry for the late reply but let me demonstrate why -(2(αβ+αγ+βα
i get my values of α+β+γ and αβ+αγ+βα from the original equation (-b/a and c/a).
The question is Find the value of α^2+β^2+γ^2. (which is the same as (α+β+γ
This simplifies to β^2-γβ+γ^2+γ^2-αγ+α^2+α^2-βα+β^2.
Which simplifies to (2(α+β+γ
Then i just substitute my values of α+β+γ and αβ+αγ+βα into the final expression to solve the whole thing.
fredrancour
Member
Hello GAF. I'm learning linear algebra. I'm doing an example problem regarding determinants. The question says to use row operations to simplify this expression to find the determinant. Based on the rules we learned, it seems like I'm either supposed to prove the determinant is zero, or to reduce the matrix to a triangular state and find the determinant that way..... but neither of those seems possible. Any ideas?
the 3x3 matrix I'm looking at is,
| 1 t t^2 |
| t 1 t |
| t^2 t 1 |
the 3x3 matrix I'm looking at is,
| 1 t t^2 |
| t 1 t |
| t^2 t 1 |
I don't know why they want you to do row reduction to find the determinant, unless you're learning how manipulating rows changes the determinant.
Anyways, If you did do row reduction to get a triangular matrix, its doable.
r2 to r2 + (-t)r1
r3 to r3 + (-t)r1
r3 to r3 +(-t)r2
None of these change the determinant, and you get (1-t^2)(1-t^2)
Which equals (1-2t^2+t^4)
If you just checked the determinant from the start you get:
1(1-t^2) - t(t-t^3) + t^2(t^2 - t^2) = (1-t^2 - t(t-t^3) = 1 - t^2 - t^2 + t^4 = (1-2t^2+t^4) so we're good.
fredrancour
Member
Dammit. I wasn't thinking of t as a constant. I just assumed I had to treat it as an unknown variable. That makes perfect sense. Thank you.
No problem, glad you've got it now.
Lion Heart
Banned
Okay I'm only asking because I think my book is wrong (I hate when this happens, total mindfuck).
Re: graphing transformations
F(x)= √x -> compressed horizontally by the factor 1/2, reflected in the y-axis,
The book has the answer negative for a, shouldn't it be negative K? so √-2(...) instead of -√2(...)?
Re: graphing transformations
F(x)= √x -> compressed horizontally by the factor 1/2, reflected in the y-axis,
The book has the answer negative for a, shouldn't it be negative K? so √-2(...) instead of -√2(...)?
triplestation
Member
i am about to finish up algebra, what should i take next? college algebra/trig or geometry?
I don't know what you mean by a or K but if you want to transform F(x)= √x by a horizontal compression of a factor of 1/2 and reflect it in the y axis, then yes, you should get:
F(x)= √-2x
The book is wrong if it has F(x)= -√2x since that would reflect it in the x axis.
youngwerther
Banned
Trig
Quick stats question that it would be great to get some help on.
THETA is uniformly distributed on [1,3]. I need to find
E[THETA | THETA < W / ALPHA]
or in words - expected value of theta conditional on theta being less than w/alpha.
I tried it using an integral over theta multiplied by the pdf of theta with w/alpha as the upper limit and 1 as the lower limit but im getting the wrong answer I think. Is this the right method?
THETA is uniformly distributed on [1,3]. I need to find
E[THETA | THETA < W / ALPHA]
or in words - expected value of theta conditional on theta being less than w/alpha.
I tried it using an integral over theta multiplied by the pdf of theta with w/alpha as the upper limit and 1 as the lower limit but im getting the wrong answer I think. Is this the right method?
triplestation
Member
aiite thanks
You should be able to use this:
P(Theta | Theta < W/alpha) = P(Theta (intersection) Theta < W/alpha) / P(Theta < W/alpha).
thequickandthedead
Member
I'm a bit confused by this. Did you verify thatis true? Because generally it is not. Also, did you expandinto? Because that doesn't seem right to me either.
Now that i go over my working, i have no idea where i got the minus signs from.
But, as Leezard also pointed out, what's the problem with α^2+β^2+γ^2 being the same as (α+β+γ
^2?Now that i go over my working, i have no idea where i got the minus signs from.
But, as Leezard also pointed out, what's the problem with α^2+β^2+γ^2 being the same as (α+β+γ
Because that's not how exponents work. (α+β+γ
^2 is (α+β+γ(α+β+γ. Expanding this doesn't give α^2+β^2+γ^2, it gives α^2+2αβ+β^2+2αγ+2βγ+γ^2Now that i go over my working, i have no idea where i got the minus signs from.
But, as Leezard also pointed out, what's the problem with α^2+β^2+γ^2 being the same as (α+β+γ
Because that's not how exponents work. (α+β+γ
What MikeDip said.
A tip for testing stuff like this on a more intuitive level is to try it with simple numbers.
(1 + 1 + 1)^2 = 3^2 = 9
1^2 + 1^2 + 1^2 = 3* 1^2 = 3
Clearly, α^2+β^2+γ^2 cannot be the same as (α+β+γ
^2.It won't work to conclusively prove an identity, but it works great for knowing what stuff doesn't work, without the need to expand parantheses. Granted, you might need to expand them afterwards to find the true identity, but that is another matter.
Partial Gamification
Banned
I'll drop this here, feel free to post-it elsewhere. Maplesoft launched an app-development pilot project.
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