Math Is Fun Forum

lindah

Member

Registered: 2010-01-25

Posts: 121

Joint Density

http://imageshack.us/photo/my-images/690/61270887.png/

Hi guys,
May I again confirm my answers/thoughts with you

Q1) I evaluated the double integral and it was equal to 1. I also substituted x=10, 20 into the function and confirmed it is >0

Q2) I drew the graph http://imageshack.us/photo/my-images/4/23301964.png/ for limits of integration

For the marginal density of x I have:

For the marginal density of y I have:

May I ask if my bounds correct in calculating this?

Q3) I had:

Q4) I feel it is related to Q3, and wanted to see if I have Q3 correct first

Thank you

Last edited by lindah (2011-06-15 14:32:09)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Joint Density

Hi;

Q1)

I am getting the same as you for the marginal density of x.

---

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.

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Re: Joint Density

For 3, 

so you are right ,gj

lindah

Member

Registered: 2010-01-25

Posts: 121

Re: Joint Density

Hi bobby and Dragonshade,

Thanks for the confirmation!

Does anyone have an idea about the marginal density of Y?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Joint Density

Hi lindah;

I am not following what you did there for the marginal density of Y.

---

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: Joint Density

Hi bobbym,
I am not sure either
May I ask what your approach to find the marginal density for y would be?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Joint Density

Hi;

May I ask what your approach to find the marginal density for y would be?

Do not laugh, I originally did this one like this:

This evaluates to a scalar, which confuses me.

---

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: Joint Density

Yes, that is what I originally got as well, which I do not think is right.

I got a similar question in my assignment just passed, and we had to find the limits by drawing out those bounds, like you would when dealing with double integrals.
So I tried that approach above, but it seems like over-complicating things.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Joint Density

Hi;

I have never seen one come out like that. But it is the only way I know how to do marginal densities.

---

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: Joint Density

Hi bobby,

Thanks for the feedback. I have never seen it the way I do it either, but I've never got a scalar as an answer for other similar questions.
Maybe it is that simple, I certainly hope so!!!

For part 4 of the question:
Using part 3) of the question, if X=12, then

However I am uncertain how to proceed to obtain P(Y>8). May I ask if you have any suggestions?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Joint Density

Hi;

That checks out, provided 3 is okay.

---

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.