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#10201 2013-04-17 05:20:09

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Okay, see you later.

#10202 2013-04-17 10:01:42

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Also I think I know the solution to the cake problem, it is a lot easier than I thought. I'll post the solution tomorrow.

#10203 2013-04-17 14:21:49

bobbym
Administrator

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Re: Linear Interpolation FP1 Formula

Hi;

Okay thanks, I have been unable to find any similar problem.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#10204 2013-04-18 00:59:51

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Nothing from adriana yet, 4 days ago now.

Here's the problem again just as a reminder:

---

The cakes in our canteen each contain exactly four currants, each currant being randomly placed in the cake. I take a proportion X of a cake where X is a random variable with density function

f(x) = Ax

for 0 ≤ x ≤ 1, where A is a constant.

(i) What is the expected number of currants in my portion?
(ii) If I find all four currants in my portion, what is the probability that I took more than
half the cake?

---

(i)



So f(x) = 2x.



The 4 currents are randomly distributed, so the expected number of currents in my portion is 4*(2/3) = 8/3.

(ii) If I take a proportion x of cake, the probability that a currant fell into it is clearly also x. The currant is either in the slice, or not in the slice. So we have a binomial distribution for the number of currants C ~ B(n, p), with p = x and n = 4. So P(C = 4) = x4. The probability distribution for a proportion X AND having 4 currants, is 2x*x4 = 2x5.

Then we just use P(A n B) = P(A|B)P(B), for which I am getting 63/64.

#10205 2013-04-18 01:09:14

bobbym
Administrator

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Re: Linear Interpolation FP1 Formula

Uh oh! I like the reasoning for the 2x^5. I think that solves that. But why not use the integral idea that toasted fellow did?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#10206 2013-04-18 01:15:31

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

That's what I did -- it's a little strange because here we are kind of using individual values in a continuous distribution. You obtain P(4 currants in portion AND more than half a portion) by integrating 2x5 between 1/2 and 1. P(4 currants in portion) is obtained just by integrating 2x5 between 0 and 1, since the size of the portion doesn't matter for that probability. Putting that together yields the same answer toasted-lion got.

#10207 2013-04-18 01:19:26

bobbym
Administrator

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Re: Linear Interpolation FP1 Formula

Sure wish we had a few more of these type to try out your idea on..


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#10208 2013-04-18 01:20:50

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I might come across some more in the 916 more STEP questions I have to do. It is going to be a long summer...

#10209 2013-04-18 01:22:40

bobbym
Administrator

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Re: Linear Interpolation FP1 Formula

I do not know how to phrase the problem to search for more. In the meantime would you mind writing up your full solution for it.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#10210 2013-04-18 01:24:31

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

My solution is basically the same as toasted-lion's on The Student Room, the only difference is I explained where the x^4 bit came from...

#10211 2013-04-18 01:29:51

bobbym
Administrator

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Re: Linear Interpolation FP1 Formula

Okay, then I will use that one with your explanation. I think it is done.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#10212 2013-04-18 01:43:32

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Okay, I have ticked it off my spreadsheet now.

No comment from adriana about the question. I think I will leave her to figure it out. (That being said, she is scared stiff of STEP III.)

#10213 2013-04-18 01:47:07

bobbym
Administrator

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Re: Linear Interpolation FP1 Formula

Good, good, you will be there to maybe comfort her. Tell her it is not possible to explain them with an email or chat. It must be done with paper and pencil and ...


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#10214 2013-04-18 01:51:28

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

And...?

#10215 2013-04-18 01:57:56

bobbym
Administrator

Offline

Re: Linear Interpolation FP1 Formula

Hmmm, can only be done in person is the point.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#10216 2013-04-18 02:06:55

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

It sounds like a nigh impossible task...

#10217 2013-04-18 02:10:46

bobbym
Administrator

Offline

Re: Linear Interpolation FP1 Formula

Well if you have explained that too her what other choice does she have but to plan something more intimate?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#10218 2013-04-18 02:12:24

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

She could say that she will just not do the question, as there are 1166 others and she is not trying to do all the questions at any rate...

#10219 2013-04-18 02:13:59

bobbym
Administrator

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Re: Linear Interpolation FP1 Formula

Then you are alleviated from having to explain it to her.

The point is to arrange a meeting not to discuss math by email, is it not?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#10220 2013-04-18 09:15:11

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I don't know, at the moment I'm not sure what I want to do. Part of me just wants to permanently ignore her, completely forget about her. I don't think she is worth the pursuit. There is now 0 benefit from knowing her.

#10221 2013-04-18 09:29:37

anonimnystefy
Real Member

Online

Re: Linear Interpolation FP1 Formula

Hi zetafunc.

You are studying at the Cambridge university, right?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

#10222 2013-04-18 10:51:01

bobbym
Administrator

Offline

Re: Linear Interpolation FP1 Formula

Hi;

I would say -5 is closer to it.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#10223 2013-04-18 18:53:26

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Nope, I was rejected by Cambridge -- for a reason my school found very controversial. I am going to UCL instead, and then maybe go there for my Masters degree instead.

Knowing her does mean she won't be put out of my mind; but I agree, nothing good really comes from talking to her anymore. I wonder if she's told her BF about me at all. Some of the stuff she used to say to me, you'd think that I was her BF! Oh well, I failed this time, but I will get another opportunity at some point, probably.

#10224 2013-04-18 23:54:20

bobbym
Administrator

Offline

Re: Linear Interpolation FP1 Formula

Probably? I have known mere bumpkins, guys that were barely human that had dozens of opportunities.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#10225 2013-04-19 00:21:51

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

You still read/hear about people who never had any opportunities though, into their middle-ages.

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