Let X1, X2 be a random sample from the Cauchy distribution with pdf f(x

Chapter 6, Problem 6.9-6

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Let X1, X2 be a random sample from the Cauchy distribution with pdf f(x | 1, 2) = 1 2 2 2 + (x 1)2 , < x < , < 1 < , 0 < 2 < . Consider the noninformative prior h(1, 2) 1 on that support. Obtain the posterior pdf (except for constants) of 1, 2 if x1 = 3 and x2 = 7. For estimates, find 1, 2 that maximizes this posterior pdf; that is, find the mode of that posterior. (This might require some reasonable trial and error or an advanced method of maximizing a function of two variables.)

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