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Joint probability distribution

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.

Solution Summary

Joint probability distribution is investigated to find the expected value, variance, and the correlation between X1 and X2. The solution was rated '5/5' by the student who posted the questions originally.