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March 14th, 2016, 01:55 AM  #1 
Senior Member Joined: Jan 2014 Posts: 196 Thanks: 3  One Dimensional Integral Expression for Joint Distribution
Suppose that $\displaystyle X $and$\displaystyle Y$ are independent random variables with probability density functions $\displaystyle f_X$ and $\displaystyle f_Y $. Determine a onedimensional integral expression for $\displaystyle P\{X + Y < x\}$. I am trying to model this from the text where the author computed $\displaystyle P\{X<Y\}$ I am not sure if this is the best example to use. I also want to use $\displaystyle F_{X+Y}(a) = P \{X + Y \leq a\}$ but I don't think I can use that because the problem show that $\displaystyle X + Y $ is $\displaystyle < x$ thank you for any help! 
March 14th, 2016, 02:59 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,804 Thanks: 715 
Standard problem  solution is convolution of the density functions.


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dimensional, distribution, expression, integral, joint 
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