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**Valle18****Guest**

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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,493

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,493

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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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,531

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,493

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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**Valle18****Guest**

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

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,493

Hi;

It is not a particularly good book.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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