Finding the domain of a changed pdf

Identity · 2009-09-01 19:41:39

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)

juriguen · 2009-09-01 20:53:14

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)

Identity · 2009-09-01 21:25:25

Oh I made another mistake with the area XD
But now I know how to find the domain
Thanks so much juriguen!

juriguen · 2009-09-01 21:32:37

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

Identity · 2009-09-02 01:23:36

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

abbies · 2009-09-02 01:52:30

hi a no the anser

Math Is Fun Forum

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

Finding the domain of a changed pdf

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

Re: Finding the domain of a changed pdf

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

Re: Finding the domain of a changed pdf

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

Re: Finding the domain of a changed pdf

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

Re: Finding the domain of a changed pdf

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

Re: Finding the domain of a changed pdf

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