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#1 2014-04-23 08:26:45

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!

#2 2014-04-23 10:44:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

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.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2014-04-23 11:21:38

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,544

Re: Joint density probability problem

I got that answer too.

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


“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

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#4 2014-04-23 11:26:00

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#5 2014-04-23 12:11:14

ShivamS
Member
Registered: 2011-02-07
Posts: 3,555

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!

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#6 2014-04-23 12:51:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

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!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#7 2014-04-23 15:23:10

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!

#8 2014-04-23 15:46:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,238

Re: Joint density probability problem

Hi;

It is not a particularly good book.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Offline

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