Math Is Fun Forum

tinbird

Member

Registered: 2010-11-02

Posts: 11

Joint density function, please help to solve

A restaurant operates both a drive-in facility and a walk-in facility. On a randomly
selected day, let X and Y respectively be the portions of the time that the drive-in and
walk-in facilities are in use, and suppose that the joint density function of these
random variables is:

f XY(x,y)= {2/3(x+2y),  0 ≤ x ≤ 1,0 ≤ y ≤ 1
                                  0,    elsewhere}

a. Find the marginal density function of X and Y.
b. Find the probability that the drive-in facility is busy less than one-half of the
time.

Last edited by tinbird (2010-11-03 21:16:29)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Joint density function, please help to solve

Hi tinbird;

I am not understanding your question. Is not the Marginal density function of f(x,y) for X just.

And for Y

I have shortened the usual intervals of plus and minus infinity to 0 - 1 to suit your problem.

Do you mean you cannot integrate those two, or you did not know the formulas?
Cause that is a more fundamental question. You have not shown any work so I do not know where you are stuck.

Also there are strange symbols in your post! Are they missing characters? I have deleted them.

---

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.

tinbird

Member

Registered: 2010-11-02

Posts: 11

Re: Joint density function, please help to solve

i don't know the formulas and the solution of the question.
fXY are subscript as you have mentioned in your email. i could not make it in subscript.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Joint density function, please help to solve

Hi;

You know how to do this integration though?

What textbook are you using? Title and author.

---

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.

tinbird

Member

Registered: 2010-11-02

Posts: 11

Re: Joint density function, please help to solve

yes i know the integration but if you can tell me that which is the part a and b formuls i will solve. i took admission in MS and my first maths subject i am week in it. if you can solve i will be very grateful

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Joint density function, please help to solve

Hi;

For a)

This is the marginal density for X.

This is the marginal density for Y.

For b)

Mind you I am not sure of a and even less sure of b. But that is what I would do.

Again, I ask what textbook are you using?

---

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.

tinbird

Member

Registered: 2010-11-02

Posts: 11

Re: Joint density function, please help to solve

erwin krezig

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Joint density function, please help to solve

Hi;

You mean Erwin Kreyszig?

And the title and edition?

---

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.

tinbird

Member

Registered: 2010-11-02

Posts: 11

Re: Joint density function, please help to solve

yes 8th edition

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Joint density function, please help to solve

We are talking about Advanced Engineering, cause I have the ninth edition.

---

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: 10,583

Re: Joint density function, please help to solve

Hi bobbym,

There's another post by tinbird but I don't understand his notation:

F_X(x)

What if F here, please?

Bob

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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 density function, please help to solve

Hi Bob;

That notation is for statistics. He is asking for the Maginal 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.

Divagirl

Guest

Re: Joint density function, please help to solve

Hi I'm new and I don't know how to get a username or a password.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Joint density function, please help to solve

Hi Divagirl;

Look up at the top of the page and click register. Pick any username and any password you want.
You will need an email address. When you are registered go to Introductions and introduce yourself by writing something about you.
That is all there is to it.

Hope to see you and welcome to the forum.

---

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.