This is the convolution [itex]F_X[/itex] and [itex]f_Y[/itex]. The density of Z is found simply by differentiating [itex]F_Z[/itex] wrt z and it gives the convolution of [itex]f_X[/itex] and [itex]f_Y[/itex].
There is probably a way to understand something from this and gain some insights about the relation btw the sum of two random variables.
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