Question: 27. (a) Suppose that the continuous random variables X and Y are independent with probability density functions f and g, both of which are symmetric

27.

(a) Suppose that the continuous random variables X and Y are independent with probability density functions f and g, both of which are symmetric about zero.

(i) Find the joint probability density function of (U, V ), where U = X and V = Y/X.

(ii) Show that the marginal density function of V is fV (v) = 2 Z

∞

0 x f (x)g(xv) dx.

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