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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: 107,161

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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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: 107,161

### Re: Probability density question

I did it this way:

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.

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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: 107,161

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #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: 107,161

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #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: 107,161

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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