Find the mean and variance of the continuous random variable X with probability density function given by 3x, x 2 1, 0, fx(x) = otherwise. A new random variable Y is defined by the relation Y = X1. Find the cumulative distribution function of Y, and hence derive its probability density function. Verify that, for X and Y as given above, E(XY) + E(X) E(Y), and explain why this result holds in this particular example.

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