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    Joint probability distribution

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    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.

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    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.