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#51 2012-11-07 09:18:43

bobbym

Online

Re: Expectation

What!!!!! Then you can never understand why I vote!

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#52 2012-11-07 09:21:15

anonimnystefy
Real Member

Online

Re: Expectation

Okay.

Got a new problem?

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#53 2012-11-07 09:23:47

bobbym

Online

Re: Expectation

My, we are in a talkative mood today.

What is the expected number of throws of a single die before a (1,1) comes up?

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#54 2012-11-07 09:27:37

anonimnystefy
Real Member

Online

Re: Expectation

42?

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#55 2012-11-07 09:31:47

bobbym

Online

Re: Expectation

Hi;

Two ways to justify that?

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#56 2012-11-07 09:34:19

anonimnystefy
Real Member

Online

Re: Expectation

Yup! A formula just like yours for the last problem and a Markov chain.

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#57 2012-11-07 09:37:16

bobbym

Online

Re: Expectation

I am putting my turban on my head. I am saying the magic words. Sorry, it is not working, I can not see your solution.

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#58 2012-11-07 09:45:33

anonimnystefy
Real Member

Online

Re: Expectation

Don't you believe me?

Markov chain:
((5/6,1/6,0);(5/6,0,1/6);(0,0,1))

A formula:
E=5/6 * (E+1) + 1/6 * 5/6 * (E+2) + 1/6 * 1/6 * 2

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#59 2012-11-07 09:49:43

bobbym

Online

Re: Expectation

Very good! The young learn quickly.

Want more?

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#60 2012-11-07 09:59:24

anonimnystefy
Real Member

Online

Re: Expectation

Of course! I have a feeling the next problem will be devilish...

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#61 2012-11-07 10:03:12

bobbym

Online

Re: Expectation

Oh yes! Hellish.

Cards from a well shuffled deck are dealt to you one at a time. What is the expected number of cards till you hold 10 hearts?

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#62 2012-11-07 10:08:15

anonimnystefy
Real Member

Online

Re: Expectation

It seems like it is just meant to confuse me, because I am getting 52 (assuming the standard number of cards in the deck)...

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#63 2012-11-07 10:09:31

bobbym

Online

Re: Expectation

Yes, it is designed to confuse you and it has. Can you not get 10 hearts in under 52 cards?

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#64 2012-11-07 10:15:34

anonimnystefy
Real Member

Online

Re: Expectation

You almost got me fooled there. I think the answer is 53/2.

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#65 2012-11-07 10:19:21

bobbym

Online

Re: Expectation

Hi;

That is not correct.

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#66 2012-11-07 10:21:28

anonimnystefy
Real Member

Online

Re: Expectation

Oh, wait! I tought it said 10 of hearts. Let me try again.

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#67 2012-11-07 10:34:56

anonimnystefy
Real Member

Online

Re: Expectation

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#68 2012-11-07 10:38:52

bobbym

Online

Re: Expectation

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#69 2012-11-07 10:43:57

anonimnystefy
Real Member

Online

Re: Expectation

Found it from the definition of expectation:

Sum[i*Binomial[13,10]*10*Binomial[39,i-10]*(i-1)!*(52-i)!/52!,i,10,52]

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#70 2012-11-07 10:46:41

bobbym

Online

Re: Expectation

Hi;

That is very good, I did not know that one. And another way is?

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#71 2012-11-07 10:48:54

anonimnystefy
Real Member

Online

Re: Expectation

I have no idea.

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#72 2012-11-07 10:52:49

bobbym

Online

Re: Expectation

The negative hypergeometric distribution is another way.

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#73 2012-11-07 11:04:52

anonimnystefy
Real Member

Online

Re: Expectation

I have not even a slightest idea what that is.

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón

#74 2012-11-07 11:07:05

bobbym

Online

Re: Expectation

The discrete distributions borrowed from statistics are of great help.

In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.

#75 2012-11-08 00:39:14

anonimnystefy
Real Member

Online

Re: Expectation

I still have no idea what that is.

Do you have a new problem?

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
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón