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March 23rd, 2010, 10:49 AM  #1 
Member Joined: Jan 2010 Posts: 43 Thanks: 0  Joint probability distribution of random variables
Let X and Y be two independent exponential random variables with distinct parameters ? and ?. Find the density of X+Y. I know that for the single variable case the exponential random variable is usually given by f(x)=?e^(?x) if x>0 and f(x)=0 for x<0. I'm unsure how to find the density (i know I need to integrate both for X and Y) but I don't know how to combine these to find the density X+Y. Any help is greatly appreciated. Thanks!

March 23rd, 2010, 06:47 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,665 Thanks: 651  Re: Joint probability distribution of random variables Quote:
Let f(x) and g(x) be the density functions of X and Y. Let h(x) be the density function of X+Y. Then: h(x)= ?g(u)f(xu)du.  

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