Suppose that X, Y are jointly continuous random variables with the joint probability density function – f(x, y) = { 12xy(1 ? x) if 0 < x < 1, 0 < y < 1 0 otherwise (a) Are X and Y independent? (b) Find the expected value of the product X · Y.
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The marginal density function of X, fX(x), is obtained by integrating f(x, y) over all possible values of y, and similarly for Y. The marginal density function of X is: fX(x) = ∫ from 0 to 1 of 121y(1-x) dy = 121 * [1/2 - x/2] = 60.5 - 60.5x for 0 < x < 1 The Show more…
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