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## Homework Statement

X is uniform [e,f] and Y is uniform [g,h]

find the pdf of Z=X+Y

## Homework Equations

f_z (t) = f_x (x) f_y (t-x) ie convolution

## The Attempt at a Solution

Obviously the lower pound is e+g and the upper bound is f+h

so it is a triangle from e+g to f+h. The tip of the triangle still in the center of the distribution i.e. .5[e+g+f+h)

so would the pdf be t for e+g< t < .5[e+g+f+h]

g+h - t for .5[e+g+f+h] <t <g+h

and 0 otherwise?