The proportions X and Y of two chemicals found in samples of

The proportions X and Y of two chemicals found in samples of an insecticide have the joint pdf f(x1, x2) = { 2 0 for 0 LE x1 LE 1,0 LE x2 LE 1,0 LE x1 + x2 LE 1, elsewhere The random variable Y = 2X1 + 3X2 denotes the proportion of the inspector due to both chemicals combined. Pr (Y GE 1); Find an interval in which values of Y should lie for at least 60% of sample of insecticide.

Solution