# joint prob density?

• August 10th 2010, 09:34 AM
bluesblues
joint prob density?
in ref to earlier thread http://www.mathhelpforum.com/math-he...tml?pagenumber=

I have stumbled upon a question which poses an identical problem but not in the form of an exam question therefore i suppose you could sketch it although from the simplicity of it i doubt this is really necessary.

If someone could show how they obtained this answer,,,and then give a valid proof to a valid method for my previous thread i'd appreciate the help,,

Q: Random variables x and y have jonint density function exp(-x-y) x.y>o

findp(x>y) answer back of book is 1/2
• August 10th 2010, 11:17 AM
yeKciM
Quote:

Originally Posted by bluesblues
in ref to earlier thread http://www.mathhelpforum.com/math-he...tml?pagenumber=

I have stumbled upon a question which poses an identical problem but not in the form of an exam question therefore i suppose you could sketch it although from the simplicity of it i doubt this is really necessary.

If someone could show how they obtained this answer,,,and then give a valid proof to a valid method for my previous thread i'd appreciate the help,,

Q: Random variables x and y have jonint density function exp(-x-y) x.y>o

findp(x>y) answer back of book is 1/2

same as there :D

$\displaystyle \int _{0} ^{\infty} \;dy \int _{0} ^{y} e^{-x-y} \;dx$

after solving :

$\displaystyle \int _{0} ^{y} e^{-x-y} \;dx = -\sinh{y} + \sinh{2y} +\cosh{y} -\cosh{2y}$

and then :

$\displaystyle \int _{0} ^{\infty} (\cosh{y}-\cosh{2y}-\sinh{y} + \sinh{2y})\;dy = \frac {1}{2}$

P.S. hope u know to work with hyperbolic functions :D

just to note that

$\displaystyle \int e^{(-x-y)} dx =\int e^{(-x-y)} dy = -e^{(-x-y)} ==\sinh{(x+y)} - \cosh{(x+y)}$
• August 10th 2010, 12:09 PM
bluesblues
yeh thanks everyone :)