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## #1 2009-09-01 19:41:39

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

### Finding the domain of a changed pdf

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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## #2 2009-09-01 20:53:14

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

### Re: Finding the domain of a changed pdf

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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## #3 2009-09-01 21:25:25

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

### Re: Finding the domain of a changed pdf

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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## #4 2009-09-01 21:32:37

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

### Re: Finding the domain of a changed pdf

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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## #5 2009-09-02 01:23:36

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

### Re: Finding the domain of a changed pdf

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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## #6 2009-09-02 01:52:30

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

### Re: Finding the domain of a changed pdf

hi  a no the anser

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