Math Is Fun Forum

Valle18

Guest

Joint density probability problem

Hello, this is my first time submitting a problem on here so let me know if there is any more information I need to give about this problem.

1) Let X denote the reaction time, in seconds, to a certain stimulant and Y denote the
temperature (0 F) at which a certain reaction starts to take place. Suppose that two random
variables X and Y have the joint density:

f(x,y) = 4xy, 0<x<1 , 0<y<1 and 0 elsewhere

Find
a. P(0 ≤ X ≤ ½ and ¼ ≤ Y ≤ ½ )

Here is my solution:

P(0 ≤ X ≤ ½ and ¼ ≤ Y ≤ ½ ) =  ∫∫4xy dx dy  =>   4∫∫xy dx dy 
                                            =>  4∫∫ (x^2/2) dy   =>  4∫ (.25y/2) dy   =>  4 ∫ (y^2/16)   = >   4(.25/16  -  .0625/16)   =>  .046875

I'm looking for someone to check and see if I got the correct solution since this is my first time doing a problem like this and I can't find the answer to it.

Thanks!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Joint density probability problem

Hi;

I am getting for a , 3 / 64 = 0.046875.

and I can't find the answer to it.

Check Probability and Statistics for Engineers and Scientists.

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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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Joint density probability problem

I got that answer too.

Is that the Devore book we were talking about, bobbym?

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Joint density probability problem

Hi;

No, this book is by Walpole.

---

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.

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Joint density probability problem

Bobbym, that is exceptional if you can tell the name of the book in which the problem is present in!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Joint density probability problem

Nope, I have that book. Just had to do a little search of the the joint probability section. If I have learned anything in 400 years it is that whenever you see something amazing suspect a trick. Remember Feynman, he was kind enough to tell us a secret to excellence. Einstein in his own cryptic way gave us another hint. Use them!

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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.

Valle18

Guest

Re: Joint density probability problem

I'll check out that book next time when I'm looking for something. Thanks for the help!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Joint density probability problem

Hi;

It is not a particularly good book.

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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.