## Search found 290 matches

- Sat Sep 15, 2012 3:58 am UTC
- Forum: Mathematics
- Topic: Sum of weighted binomial distribution
- Replies:
**10** - Views:
**2492**

### Re: Sum of weighted binomial distribution

Each item has a 1/n chance of matching craft number and level. There are n such items, so the expected number of matchings is n (1/n). That's... not a proof to me, mate. That's not proving anything. That's just saying some words and waving hands. *Why* is it that the sum from 0 to n of k * p(k) is 1?

- Sat Sep 15, 2012 3:53 am UTC
- Forum: Mathematics
- Topic: Sum of weighted binomial distribution
- Replies:
**10** - Views:
**2492**

### Re: Sum of weighted binomial distribution

Deedlit wrote:The expected number of successes is E = Sum{1 to n} k p(k).

But the expected number of sucesses is n * (1/n) = 1.

I get the first sentence, but not the second. How do you arrive there?

- Sat Sep 15, 2012 3:44 am UTC
- Forum: Mathematics
- Topic: Sum of weighted binomial distribution
- Replies:
**10** - Views:
**2492**

### Re: Sum of weighted binomial distribution

jestingrabbit wrote:Looks like its the binomial expansion of ((n-1)/n + 1/n)^n = 1^n = 1

It is!

But I'm weighting it, you see.

It's the binomial expansion, but weighted.

That's the point.

That's the reason I'm wondering how it ends up working out to also be 1 when summed.

- Fri Sep 14, 2012 9:23 pm UTC
- Forum: Mathematics
- Topic: Sum of weighted binomial distribution
- Replies:
**10** - Views:
**2492**

### Re: Sum of weighted binomial distribution

As far as I can tell, your specific example (99/100)^100 * (1/99)^k * (100 choose k) doesn't match the general case ((n-1)/n)^(n-k) * (1/n)^k * (n choose k) you posted. (I think it's a pretty minor error in the specific example though, and so won't affect the results.) But it does! for n = 100, ((n...

- Fri Sep 14, 2012 6:20 pm UTC
- Forum: Mathematics
- Topic: Sum of weighted binomial distribution
- Replies:
**10** - Views:
**2492**

### Sum of weighted binomial distribution

My mathematical curiosity was piqued when I was just doing some normal number investigation. Background: Friend on TF2 likes to collect craft number items where the craft number is equal to the level of the item - craft numbers will only display on the item itself between 1 and 100, and level is bet...

- Mon Jan 02, 2012 12:25 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0997: "Wait Wait"
- Replies:
**115** - Views:
**32954**

### Re: 0997: "Wait Wait"

You know, it took me a while to realize that xkcd comics haven't been good. The turning point was a particular incident - a normal discussion with one of my peers in the undergraduate program in Mathematics. I mentioned xkcd somehow, he professed confusion, so I endeavoured to show him what I believ...

- Sat Dec 31, 2011 8:08 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0997: "Wait Wait"
- Replies:
**115** - Views:
**32954**

### Re: 0997: "Wait Wait"

I registered on these forums just to say that this comic was terrible.

- Mon May 02, 2011 5:35 am UTC
- Forum: Mathematics
- Topic: Must a ring have multiplicative identity?
- Replies:
**8** - Views:
**2891**

### Re: Must a ring have multiplicative identity?

I learned it as "ring" and "ring with unity". It's a contested convention!

- Thu Feb 03, 2011 9:44 pm UTC
- Forum: Mathematics
- Topic: Fun Math Riddles
- Replies:
**54** - Views:
**6355**

### Re: Fun Math Riddles

Back on topic, this is an interesting riddle, if none of them have heard it before: As I was going to St Ives I met a man with seven wives Each wife had seven sacks Each sack had seven cats Each cat had seven kits Kits, cats, sacks, wives How many were going to St Ives? It cannot be determined from...

- Fri Jan 14, 2011 4:10 am UTC
- Forum: Mathematics
- Topic: Geometry problem (triangles)
- Replies:
**14** - Views:
**1663**

### Re: Geometry problem (triangles)

They're not circles - they're 90-gons.

- Tue Jan 11, 2011 2:24 am UTC
- Forum: Mathematics
- Topic: Binary fractal
- Replies:
**14** - Views:
**1999**

### Re: Binary fractal

It is created by cycling through binary numbers with the leading zeros (0000, 0001, 0010, 0011, 0100 etc.), incrementing the x value if it is a zero, and the y value if it is a 1 (screen coords, shape is the same).

Could you explain this better? What numbers?

- Sat Jan 08, 2011 8:02 am UTC
- Forum: Mathematics
- Topic: Syntax for mathematical logic
- Replies:
**5** - Views:
**833**

### Re: Syntax for mathematical logic

I'm not entirely sure what the point of all this is, or what you're even asking, but, if my guess is right:

[math](wa \iff a) ∧ (wb \iff b)[/math]

[math](wa \iff a) ∧ (wb \iff b)[/math]

- Sat Jan 01, 2011 12:11 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0841: "Audiophiles"
- Replies:
**266** - Views:
**51688**

### Re: 0841: Audiophiles

Is there some other magical way of communicating with somebody that is as cheap and easy as a cell phone, but which has higher audio quality? Yes, it is called the land-line telephone which uses a 64kbps channel. The sample rate is 8000Hz (with a frequency cut-off of about 3kHz) and a resolution of...

- Fri Dec 31, 2010 7:19 pm UTC
- Forum: Mathematics
- Topic: Cardinalities
- Replies:
**15** - Views:
**1888**

### Re: Cardinalities

Hahaha whoops ignore everything I said.

Sigh, I hate it when I'm completely wrong. I was only looking at "10^(-n)". :/

Sigh, I hate it when I'm completely wrong. I was only looking at "10^(-n)". :/

- Fri Dec 31, 2010 5:56 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0841: "Audiophiles"
- Replies:
**266** - Views:
**51688**

### Re: 0841: "Audiophiles"

I mostly dropped in on this discussion to see all the audiophiles say things like "I'm no audiofile but if your listening to utube rips at 96 kdps your a loser jerk and not a ubur-cool audiofile like me!" Sadly, I have not been disappointed. Audiophiles are nothing if not predictable, and...

- Fri Dec 31, 2010 5:16 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0841: "Audiophiles"
- Replies:
**266** - Views:
**51688**

### Re: 0841: "Audiophiles"

While it is made obvious that we are supposed to dislike her for her disdain, this guy apparently listens to 96 kbps youtube rips And the woman is listening to the 12 kbps mobile phone noise by even talking to the man, so not everyone has constantly high (or even mediocre) standards. Lighten up. Th...

- Fri Dec 31, 2010 4:55 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0841: "Audiophiles"
- Replies:
**266** - Views:
**51688**

### Re: 0841: Audiophiles

god, randall is like the last person who should be criticizing people for being snobs I'll bite. How is Randall a snob? He occasionally mocks technologically illiterate and ignorant people for not caring about how or why they use their technology, and then hypocritically mocks someone for taking a ...

- Wed Dec 29, 2010 5:17 pm UTC
- Forum: Mathematics
- Topic: Cardinalities
- Replies:
**15** - Views:
**1888**

### Re: Cardinalities

Sorry, I worded this badly, let me try again. The function: f(x) = x/(10^ceil(log10(x))) returns a real number number between 0 and 1. z = f(x) A is the set of all possible values of z where x is a positive integer. This has a one to one correspondence with the set of all integers meaning it has a ...

- Sat Dec 18, 2010 10:10 pm UTC
- Forum: Mathematics
- Topic: Game Theory at a high school level
- Replies:
**11** - Views:
**2570**

### Re: Game Theory at a high school level

http://en.wikipedia.org/wiki/English_pronunciation_of_Greek_letters For some reason the British have come up with their own nonsense pronunciation, while the Americans at least try to resemble the original. And as any sane person will testify that "bee-tah" sounds ridiculus, why don't we ...

- Tue Dec 14, 2010 7:55 pm UTC
- Forum: Mathematics
- Topic: Game Theory at a high school level
- Replies:
**11** - Views:
**2570**

### Re: Game Theory at a high school level

Arariel wrote:My only gripe with him is his insistence to pronounce β as "bee-tah"

If I'm not mistaken, I believe that is the more faithful way of saying it.

- Fri Nov 19, 2010 1:56 am UTC
- Forum: Mathematics
- Topic: Stand-Up Quiz
- Replies:
**5** - Views:
**988**

### Re: Stand-Up Quiz

pTea wrote:My English teacher has a very interesting way of quizzing his class.

My Homework has a very obvious way of being solved.

- Fri Nov 19, 2010 1:23 am UTC
- Forum: Mathematics
- Topic: A question about rings
- Replies:
**10** - Views:
**960**

### Re: A question about rings

R can't be finite for an element to have two right inverses in the first place. This is the bit that I was having troubles with actually. It took me a while before I realized that it follows from associativity, since there just aren't enough elements to go around :P. I wonder if we can show that th...

- Thu Nov 11, 2010 1:03 am UTC
- Forum: Mathematics
- Topic: Topology HW question
- Replies:
**9** - Views:
**1606**

### Re: Topology HW question

One useful trick when using the inverse image of open sets is to look at the preimage of a basis for the topology of the codomain. If I remember rightly, it can be proven that if the preimages of the basis elements remain open, then the preimages of all open sets remain open. I could be wrong -- I ...

- Sun Oct 31, 2010 7:10 pm UTC
- Forum: Mathematics
- Topic: My idea on why math is hard...
- Replies:
**28** - Views:
**3907**

### Re: My idea on why math is hard...

The best case scenario isn't when you're good at thinking math when you're doing math problems for school or when you're learning at school - it's when you're thinking math always. Looks like you are, so it would seem that you're doing fine.

- Sat Oct 30, 2010 4:50 pm UTC
- Forum: Mathematics
- Topic: Definition of "choice in function" ?
- Replies:
**1** - Views:
**722**

### Re: Definition of "choice in function" ?

Uh.

What?

It seems that your question is... how many distinct functions f : X -> X are there for a finite set X? The answer is |X|

What?

It seems that your question is... how many distinct functions f : X -> X are there for a finite set X? The answer is |X|

^{|X|}(alternately, the set of functions itself is X^{X})- Sat Oct 30, 2010 1:12 am UTC
- Forum: Mathematics
- Topic: How many digits of Pi do you know?
- Replies:
**445** - Views:
**107041**

### Re: How many digits of e/pi/etc you know, and your method?

The accuracy to which I know pi: 3.141592653589793238462643383 I'm not sure when or how I picked that up but it's stayed with me. I remembered the following just sitting in class in highschool bored: 2.71828182845904523536028747135266249775757247093699959574966967627724076630353547594571382178525166...

- Mon Oct 25, 2010 10:43 am UTC
- Forum: Mathematics
- Topic: I need some kind of help (Proof on Equivalence Relation)
- Replies:
**26** - Views:
**2400**

### Re: I need some kind of help (Proof on Equivalence Relation)

Really? It's how I think of relations.

- Thu Oct 21, 2010 1:11 pm UTC
- Forum: Mathematics
- Topic: Help a kid with Calculus!
- Replies:
**55** - Views:
**4612**

### Re: Calculus (more specifically Integral Calculus)

Sure! Education differs quite radically depending on location, so I still can't quite comment, but you seem well enough off if you're interested in math. Some advice, though - don't try to learn through Wikipedia. It's a great repository for mathematical knowledge when you already vaguely know the s...

- Thu Oct 21, 2010 1:03 pm UTC
- Forum: Mathematics
- Topic: Help a kid with Calculus!
- Replies:
**55** - Views:
**4612**

### Re: Calculus (more specifically Integral Calculus)

Thanks, the "F" really cleared things up, but why would F(1)-F(0) = the area? Because of the fundamental theorem of calculus, of course! so am I doing fine? Well, that should be a judgement call that you should make, not us - what level of education are you in? How are you learning these ...

- Thu Oct 21, 2010 12:56 pm UTC
- Forum: Mathematics
- Topic: Help a kid with Calculus!
- Replies:
**55** - Views:
**4612**

### Re: Calculus (more specifically Integral Calculus)

2 ) Why is \int_0^1 dx f(x) = F(1) - F(0) and what the heck is the capital F? Convention is that you place dx after the f(x), not before. F is the antiderivative of f. Its actually done both ways Oh yeah? Well, learn something new every day I guess! Then I said can't I make ...

- Thu Oct 21, 2010 12:35 pm UTC
- Forum: Mathematics
- Topic: Help a kid with Calculus!
- Replies:
**55** - Views:
**4612**

### Re: Calculus (more specifically Integral Calculus)

I'm skipping a lot because I am bored I seem to have identified your problem. 1 ) Why would the derivative of sin(3x^2+1) become 9x*cos(3x 2 +1)? Chain rule. 2 ) Why is \int_0^1 dx f(x) = F(1) - F(0) and what the heck is the capital F? Convention is that you place dx after t...

- Thu Oct 21, 2010 11:40 am UTC
- Forum: Mathematics
- Topic: Yo momma's so nerdy...
- Replies:
**40** - Views:
**7166**

### Re: Yo momma's so nerdy...

Yo momma's so fat she inspired Russell's paradox

- Thu Oct 21, 2010 11:16 am UTC
- Forum: Mathematics
- Topic: I join the blagosphere
- Replies:
**28** - Views:
**2897**

### Re: I join the blagosphere

I actually like how naturals->integers->rationals progresses from monoid->group, give it multiplication and then it's a ring->field. Then every step of the way seems like a natural extension from the previous - so, yeah, closure under subtraction (additive inverses) and division (multiplicative inve...

- Thu Oct 21, 2010 6:01 am UTC
- Forum: Mathematics
- Topic: I join the blagosphere
- Replies:
**28** - Views:
**2897**

### Re: I join the blagosphere

Constructing the integers/rationals/reals is an interesting topic. "Bam dedekind cuts, surprise you now have the reals"

It's pretty cool.

It's pretty cool.

- Mon Oct 11, 2010 2:33 am UTC
- Forum: Mathematics
- Topic: question on order relations
- Replies:
**3** - Views:
**543**

### Re: question on order relations

I'm not entirely sure why the a~=b requirement was thrown in there. Your answer should be fine.

Something to note: even if that were not a requirement, it would still not be reflexive - as it's only a relation on the integral pairs.

Something to note: even if that were not a requirement, it would still not be reflexive - as it's only a relation on the integral pairs.

- Thu Oct 07, 2010 2:50 am UTC
- Forum: Mathematics
- Topic: Topology, Product topologies and boundry
- Replies:
**21** - Views:
**2926**

### Re: Topology, Product topologies and boundry

If you meant their union... well, go ahead and try to prove it =)

- Thu Oct 07, 2010 2:43 am UTC
- Forum: Mathematics
- Topic: Topology, Product topologies and boundry
- Replies:
**21** - Views:
**2926**

### Re: Topology, Product topologies and boundry

Well, the last bit "sort of" follows from looking at the question statement - there's a hint lying there. It should then follow by considering the definition of points within a boundary. An element p is within \partial A if for all neighbourhoods U of p, \exists x\in U\ s.t\ \ x \in A and ...

- Thu Oct 07, 2010 2:35 am UTC
- Forum: Mathematics
- Topic: Topology, Product topologies and boundry
- Replies:
**21** - Views:
**2926**

### Re: Topology, Product topologies and boundry

What about the point (a, c) in [imath]X\times Y[/imath]?

- Tue Oct 05, 2010 6:21 pm UTC
- Forum: Mathematics
- Topic: Math: Fleeting Thoughts
- Replies:
**434** - Views:
**158242**

### Re: Math: Fleeting Thoughts

Consider the following two person logic game. \forall x \exists y P(x,y) Where x \in {a,b} and y \in {c,d}. Player 1 picks the x, Player 2 picks the y. Player 1 wins if the Decidable Property P is false, Player 2 wins if the property P is true. This is a two-player, two-option game, as Play...

- Mon Oct 04, 2010 10:18 pm UTC
- Forum: Mathematics
- Topic: I join the blagosphere
- Replies:
**28** - Views:
**2897**

### Re: I join the blagosphere

You put the odd numbers before the even numbers in one of your examples, but said the opposite.