
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 10th, 2017, 09:14 PM  #1 
Newbie Joined: Feb 2017 From: Corpus Christi Texas Posts: 6 Thanks: 0  Finding a probability density function from a distribution function and using it.
F(x,y)=1e^[x]e^[y]+e^[xy] So f(x,y)= e^[xy] if I did both partials over. I'm told to find P(X+Y>3) I can't quite get the bounds right. It's a double integral of f(x,y). Are the founds (3y) to (infinite) for dx And 0 to (infinite) for dy? 
February 10th, 2017, 09:41 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 923 
the pdf is actually $f_{XY}(x,y) = e^{(x+y)},~x,y \geq 0$ so $P[X+Y>3] = 1P[X+Y\leq 3] = 1\displaystyle{\int_0^\infty \int_0^{3x}}~e^{(x+y)}~dx =$ $1 \displaystyle{\int_0^3 \int_0^{3x}}~e^{(x+y)}~dx $ I leave it to you to compute this. 
February 11th, 2017, 10:53 AM  #3 
Newbie Joined: Feb 2017 From: Corpus Christi Texas Posts: 6 Thanks: 0 
Oh that makes sense why you would use the compliment . Thanks!

February 11th, 2017, 11:16 AM  #4 
Newbie Joined: Feb 2017 From: Corpus Christi Texas Posts: 6 Thanks: 0 
Mmmmmmm
Last edited by Rramos2; February 11th, 2017 at 11:35 AM. 
February 11th, 2017, 11:38 AM  #5 
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 923  do they show how they derive this? you can do the integral directly as $P[X+Y>3] = \displaystyle{\int_0^3 \int_{3x}^\infty}~e^{(x+y)}~dx + \displaystyle{\int_3^\infty \int_{0}^\infty}~e^{(x+y)}~dx$ and come up with the same answer as in post #2 
February 11th, 2017, 11:38 AM  #6 
Senior Member Joined: Sep 2015 From: USA Posts: 1,790 Thanks: 923  

Tags 
density, distribution, finding, function, probability 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Joint Probability Density Function of a Sample of A Normal Distribution  IndependentThinker  Advanced Statistics  1  February 27th, 2015 02:01 PM 
Finding probability density function  Aleks855  Advanced Statistics  3  February 19th, 2013 03:43 PM 
Help with finding density function  tnutty  Advanced Statistics  1  April 4th, 2011 01:03 PM 
Finding probability density function (pdf)  knp  Calculus  8  November 23rd, 2010 08:27 PM 
Finding probability density function (pdf)  knp  Algebra  2  December 31st, 1969 04:00 PM 