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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
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,908

### 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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,889

### Re: Joint density probability problem

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
The knowledge of some things as a function of age is a delta function.

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

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,908

### 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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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

ShivamS
Member
Registered: 2011-02-07
Posts: 3,640

### 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
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,908

### 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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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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
From: Bumpkinland
Registered: 2009-04-12
Posts: 92,908

### 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.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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