Every week, Alex receives 6 rubles allowance from his parents. He usually spends most of it buying candy. In Alex’s favorite candy store, Skittles are sold in bulk at 1 ruble per kg, and M&M’s are sold at 2 rubles per kg. Let X and Y denote the weight (in kg) of Skittles and M&M’s Alex buys, respectively. Since Skittles are cheaper, and Alex has not yet grasped the concept of quality over quantity, he always buys more Skittles than M&M’s.
Let the joint probability density function for ( X, Y ) be:

f( x, y ) = (2x + y)/C , 0 ≤ y ≤ x, x + 2 y ≤ 6,
0 otherwise.
X – Skittles, Y – M&M’s.

Find the probability distribution of the total weight of candy W = X + Y.