5. A quality control engineer found that the inner and outer diameters of their ball bearings, denoted respectively as X and Y, are random variables with E(X|Y = y) = 0.7-0.3y inches and Var(X|Y = y) = 0.0004y for all values of y. From his past experience he also knew that the mean and variance of the outer diameters were E(Y) = (0.7 inches, and Var(Y) = 0.0001 squared inches. %3D (i) What are the conditional random variables, E(X Y) and Var(X|Y)? • (ii) Find the mean of the inner diameters, E(X). • (iii) Find the variance of the inner diameters, Var(X).

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