Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#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: 81,711

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,845

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

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,711

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

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

ShivamS
Member
Registered: 2011-02-07
Posts: 3,414

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!

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,711

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#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: 81,711

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

Board footer

Powered by FluxBB