Px=0

1/8*1/8
## [1] 0.015625

Px=1

1/8*3/8 + 3/8*1/8 
## [1] 0.09375

Px=2

1/8*1/2 + 3/8*3/8 + 1/2*1/8
## [1] 0.265625

Find the distribution of the sum X1 + X2

(1/8*1/8 ) + (1/8*3/8 + 3/8*1/8) + (1/8*1/2 + 3/8*3/8 + 1/2*1/8)
## [1] 0.375