Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,737

Look at the formula for no one getting drunk. The (k-1)! is the number of them.

Now if you tell me what you are trying to do I can suggest a good means of computing the numbers.

*Last edited by bobbym (2013-03-23 22:33:11)*

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**NobodyButYou****Member**- Registered: 2013-03-23
- Posts: 8

I am trying to understand the logic behind the terms that's all.

Summation from j= 0 to n of (-1)^j/j! in the numerator is not getting into my head.

As far as my understanding goes, it computes the number of ways you can give out n names to n people without any of them having their own name.

Why do we need to multiply the summation in the numerator with P(no one getting drunk)?

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,737

All the forms there were obtained empirically. By looking at the data. There just was no other way that I could solve the problem,

As far as my understanding goes, it computes the number of ways you can give out n names to n people without any of them having their own name.

That is the number of derangements which is always an integer. Your sum there is not always an integer.

*Last edited by bobbym (2013-03-24 01:21:52)*

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**ernchung****Member**- Registered: 2016-02-26
- Posts: 14

k stands for the total no. of players , how about n?

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,737

Almost a month has gone by, you will have to refresh my memory. What is your question?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**ernchung****Member**- Registered: 2016-02-26
- Posts: 14

the general formula of the expected value in part b, u show a lot of summations in the formula, k is the total number of players, j is a dummy , how about n?

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,737

n is the counting variable and the sum adds probabilities up for each player.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**ernchung****Member**- Registered: 2016-02-26
- Posts: 14

ic, i cant find the expected value for n=100 with my scientific calculator, can u gimme a hand? ty very much

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,737

Do you mean k = 100 , not n.

I will get it for you, in the meantime to check what did you get for 10?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**ernchung****Member**- Registered: 2016-02-26
- Posts: 14

thank you i have to hand it in 1 hour later, i should ask you earlier. i got 3.5500 for k=10

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,737

Hi;

That checks with what I got for 10. For 100, I am getting 48.505

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**ernchung****Member**- Registered: 2016-02-26
- Posts: 14

Thank you~

I am re calculating it right now.

By the way, just want to know if you have learnt survival model before?

Offline

**ernchung****Member**- Registered: 2016-02-26
- Posts: 14

I would also like to know which software or calculator are you using for these questions

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,737

I am using a CAS ( Computer Algebra System ), I like Mathematica. It is not free but many universities supply it to their students. Also, there is a version of it online. There are also free ones too.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**ernchung****Member**- Registered: 2016-02-26
- Posts: 14

ok i will try it out later, have to work on the mid term exams today.

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 107,737

Ask if you need help.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline