12. Let X, Y have joint density p( x ,y) = 2f(x)f(y)F(8xy), where f is a known probability density symmetric about 0, and Fits cumulative distribution function. Then (i) p(x, y) is a probability density. (ii) X and Yeach have marginal density f and are therefore ancillary, but (X, Y) is not. (iii) X · Y is a sufficient statistic for 8. [Dawid (1977).]