Math Is Fun Forum

lindah

Member

Registered: 2010-01-25

Posts: 121

Transformation of variable

In attempting this I arrive at

Then finding the cdf of

I have:

for

So my cdf is

Then the pdf is the derivative of this

All critiques are welcome!!

Last edited by lindah (2011-06-20 22:28:47)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Transformation of variable

hi Lindah,

I don't think I've got the problem fully.

All I see is

If U is uniform in {0,1] find the cdf and pdf of root U

What am I missing?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

lindah

Member

Registered: 2010-01-25

Posts: 121

Re: Transformation of variable

Hi Bob,

That is all we were given for the question (per the past paper I am looking at).

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Transformation of variable

Hi;

How did you get the 1 for y > 1?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

lindah

Member

Registered: 2010-01-25

Posts: 121

Re: Transformation of variable

Hi;

I'm assuming it is 1 due to the definition of a cdf ranging from [0,1]. Is this a valid approach?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Transformation of variable

The PDF for U is 1 for 0 <= x <= 1 and 0 elsewhere so I would think that it should be like this.

What do you think?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

lindah

Member

Registered: 2010-01-25

Posts: 121

Re: Transformation of variable

Hi bobby,

I am not sure

I previously did it that way as per http://www.mathisfunforum.com/viewtopic.php?id=15626, but in post #11 Bob corrected it with the last part of a cdf should be 1.
I am also follows the example I found here (the very last question):
http://www.stat.cmu.edu/~larry/=stat705/test1sol.pdf

Last edited by lindah (2011-06-21 02:44:08)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Transformation of variable

Hi;

Yes, I think he is right now! Good point! Thanks for refreshing my memory. You are correct.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.