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#1 2012-10-20 10:51:29

genericname
Member
Registered: 2012-05-16
Posts: 52

Probability density question


Given a random variable X with probability density f(x) = x/8 for 0 ≤ x ≤ 4:
1) What is the probability that X is between 1 and 3?
2) Find the expected value of X

How do you find the expected value for these type of questions? In general to find the expected value you use (x*(p(x)), so does that mean you have to plug in numbers 0 to 4 and apply the same formula after? Also for number 1 I got 1/2 as an answer.

Last edited by genericname (2012-10-20 11:04:07)

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#2 2012-10-20 11:07:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,711

Re: Probability density question

Hi;

I am getting that for 1 also, for 2) I am getting 8 / 3.


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.

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#3 2012-10-20 11:22:42

genericname
Member
Registered: 2012-05-16
Posts: 52

Re: Probability density question

What is the formula for getting 8/3?

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#4 2012-10-20 11:26:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,711

Re: Probability density question

I did it this way:


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.

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#5 2012-10-20 11:42:39

genericname
Member
Registered: 2012-05-16
Posts: 52

Re: Probability density question

I'm not quite understanding it. The value of x = 0, 1, 2, 3, 4?

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#6 2012-10-20 11:45:31

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,711

Re: Probability density question

Nope, the value of x is those and everything in between them. This is a continuous function.


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.

Offline

#7 2012-10-20 11:51:38

genericname
Member
Registered: 2012-05-16
Posts: 52

Re: Probability density question

How does it come up to 8/3? (Sorry for the dumb questions)

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#8 2012-10-20 11:59:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,711

Re: Probability density question

Hi;

Did you see post #4? That is the formula. I just took the endpoints from the 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.

Offline

#9 2012-10-20 12:13:31

genericname
Member
Registered: 2012-05-16
Posts: 52

Re: Probability density question

Ah, thank you. I was overthinking it.

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#10 2012-10-20 12:15:59

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,711

Re: Probability density question

Hi;

Or maybe I am underthinking it. Anyway, hope that helps a little.


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.

Offline

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