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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 dunno?

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! smile

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! smile

Jose

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

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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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