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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,704

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.**

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

What is the formula for getting 8/3?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,704

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.**

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

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,704

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.**

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

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,704

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.**

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

Ah, thank you. I was overthinking it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 94,704

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.**

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