Let X1 and X2 denote the proportion of two different chemicals found in a sample mixture of chemicals and used as an insecticide. Suppose X1 and X2 have the joint probability density function given by:

f(x) = { 2 0 <= x1 <= 1, 0 <= x2 <= 1, 0 <= x1+x2 <= 1 0 otherwise}

Let Y = X1 + X2, that is the total proportion of the two chemicals found in a sample mixture.

a) Find E(Y) and V(Y)

b) Find an interval in which values of Y should lie for at least 50% of the samples of insecticide.

c) Find the correlation between X1 and X2 and interpret its meaning.