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) = 2*t), 0 x, x+2y= 6, zero otherwise. X-Skittles, Y - M&M's. a) Find the probability that the total weight of candy that Alex buys is over 3.6 kg. That is, find P(X+Y>3.6). b)Find the probability that the total weight of candy that Alex buys is over 4.8 kg. That is, find P(X+Y>4.8). c) Find the probability that Alex spends more than 4.8 rubles buying Skittles and M&M's. That is, find P(X+2Y> 4.8). d) Find the probability that that Alex spends more on Skittles than he spends on M&M's. That is, find P(X>2Y). (Also the probability that the weight of Skittles is more than twice the weight of M&M's.)