Let [math]X_1[/math] and [math]X_2[/math] be independent random variables with common distribution

[[math]] p_X = \pmatrix{ 0 & 1 & 2 \cr 1/8 & 3/8 & 1/2\cr}. [[/math]]

Find the distribution of the sum [math]X_1 + X_2[/math].