Friday 17 July 2015

probability - How to find the CDF of the sum of independent uniformly distributed random variables?

$X,Y$ are independent random variables with uniform distribution on $[0,1]$, and let the random variable $Z=X+Y$.




The density of $Z$ is:
$$f_{X+Y}(z)=\int_0^z f_X(x)f_Y(z-x)dx$$



What is the formula for the probability $P(Z \leq m)$?



Any help would be appreciated.



Sorry, I have no attempt.

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