Let x and y be two random variables with pdf given as

\({f_x}\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{3}}&{ -1 \le x \le 2}\\ 0&{otherwise} \end{array}} \right.\) 

\({f_y}\left( y \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{3}}&{- 2 \le x \le 1}\\ 0&{otherwise} \end{array}} \right.\)

Then pdf of random variable Z = X + Y is of form