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0 we have the simple result that S2/0 is x2 with n degrees of freedom. 1 for the variance situation, but there exists a wide class of prior distributions, satisfying conditions similar to those in that theorem, which leads to this last result as an approximation.

0 and (jv0 -1) ! times this tends, as vo -> 0, to 0-1. Hence the prior distribution suggested has density proportional to 0-1. This is not a usual form of density since, like the uniform distri- bution of the mean, it cannot be standardized to integrate to one. 2). With this prior distribution and the likelihood given by (3), the posterior distribution is obviously, e-Sh/2ee-In-1, which apart from the constant of proportionality, is (4) with vo = 0. Hence the usual form of inference made in the situation of the theorem, that is with imprecise prior knowledge, is (b) the parameter 0 is such that S2/0 is distributed in a x2distribution with n degrees of freedom.

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