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March 14th, 2016, 01:55 AM   #1
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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 one-dimensional 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!
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March 14th, 2016, 02:59 PM   #2
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Standard problem - solution is convolution of the density functions.
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