Math Is Fun Forum

tinbird

Member

Registered: 2010-11-02

Posts: 11

joint probability mass function

Suppose that the following table represents the joint probability mass function of the discrete RVs (X, Y):
    a. Compute fX(x), fY(y), fXY(x|y) and fXY(y|x).
    b. Decide whether Xand Yare independent.

pXY(x,y) --------------------- x
----------------------- 1          2      3
y ---------- 1 -------- 1/12    1/6   0
y ----------- 2 -------- 0       1/9   1/5
y----------- 3 --------- 1/18    ¼   2/15

Last edited by tinbird (2010-11-04 20:56:44)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: joint probability mass function

hi tinbird,

Im having trouble understanding this notation:

fX(x), fY(y), fXY(x|y) and fXY(y|x).

Can you define fX(x) in words please?

To prove independence you'd need to calculate probabilities; is that what these fs are?

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: joint probability mass function

Hi Bob

fX(x) in latex.

That is the Marginal Density of the Joint Density function. It is just an integral. Same thing for

fXY(x|y) and fXY(y|x)

The last 2 are not as clear. It is obviously a conditional probability.
I have been trying to get something out him but it has not worked.

---

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: joint probability mass function

hi bobbym

Thank you for that.  But his question has a table that seems to have discrete values.  So do I substitute a summation for an integral?

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: joint probability mass function

Yes, It becomes a summation rather than an integration. There is some differences. He is working from the book Advanced Engineering Mathematics by Erwin Kreyszig. I would like to see some effort and interest by him in his own homework. I am sticking to the new guidelines that you yourself help institute.

---

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: joint probability mass function

hi bobbym

Ok.

thanks again.

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

tinbird

Member

Registered: 2010-11-02

Posts: 11

Re: joint probability mass function

In latex what you have written is all ok. This was what i wanted to write like that but i dont know who you write here in this website. The x = 1,2,3 and y = 1,2,3 have  diff probabilities and yes they have to be sum up but how. our teacher says there is no single book to follow. You can study from anywhere.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: joint probability mass function

our teacher says there is no single book to follow. You can study from anywhere.

Really! An interesting hypothesis! Does he/she say why you should not study the Kreyszig book?

Here is how you use latex.

http://www.mathisfunforum.com/viewtopic.php?id=4397

or use this page that I use for my latex.

http://latex.codecogs.com/editor.php

---

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.