Normal before Student

Topic: Bayesian linear regression · more questions on this topic
‹ Errors and residuals The inverse-Gamma shape trap ›

Derive the exact sampling distribution of \widehat{\boldsymbol{\beta}} when \sigma^2 is known. Then show which replacement and standardisation produce the univariate Student pivot in Equation (10) in Bayesian linear regression–Equation (12) in Bayesian linear regression. State clearly why \widehat{\boldsymbol{\beta}} itself has not thereby become Student distributed.

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