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**Identity****Member**- Registered: 2007-04-18
- Posts: 934

Let X be a random variable with density function

Find the density fuction of

How can this be a density function if the area underneath it is not equal to 1?

Anyway... I was able to find the new density function,

, but I don't know how to logically find it's domain.The answer says the domain is

, I guess because the area under the new density function from 0 to 8 is equal to 1. But the original density function didn't have an area equal to 1 so why must this one ?Also, I think

is pretty arbitrary, how come you can't have something like ? That gives an area of 1 as well.*Last edited by Identity (2009-09-01 19:42:15)*

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**juriguen****Member**- Registered: 2009-07-05
- Posts: 59

Hi!

The area underneath the first curve is equal to 1:

And the domain is the mapping between x and y:

Jose

*Last edited by juriguen (2009-09-02 01:38:38)*

Make everything as simple as possible, but not simpler. -- Albert Einstein

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**Identity****Member**- Registered: 2007-04-18
- Posts: 934

Oh I made another mistake with the area XD

But now I know how to find the domain

Thanks so much juriguen!

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**juriguen****Member**- Registered: 2009-07-05
- Posts: 59

Haha, you're welcome!

It is curious that you calculated the area underneath f(y) correctly, and not for f(x). That for f(y) is much more difficult!

Jose

Make everything as simple as possible, but not simpler. -- Albert Einstein

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**Identity****Member**- Registered: 2007-04-18
- Posts: 934

juriguen wrote:

Haha, you're welcome!

It is curious that you calculated the area underneath f(y) correctly, and not for f(x). That for f(y) is much more difficult!

Jose

Yes, I tend to overlook simple things because I don't think they are worth my time. Perhaps I should learn better

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**abbies****Member**- Registered: 2009-09-01
- Posts: 3

hi a no the anser

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