A normal statistic

Topic: Exponential families and conjugacy · more questions on this topic
‹ Factorisation and data reduction Reading conjugacy from a kernel ›

For iid \operatorname{N}(\mu,\sigma^2) observations with both parameters unknown, factor the joint density and show that (\sum_iX_i,\sum_iX_i^2) is sufficient. Rewrite this statistic in terms of (\overline X,\sum_i(X_i-\overline X)^2) and prove that the two versions contain the same information.

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