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This page is from Pattern Recognition by Bishop. What is the explanation for equations 1.70. 1.71 and 1.72?

Edit: The distributions are all Gaussian.

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Since you only mention that their Gaussian, here is a screenshot depicting the relationship of gaussian conjugate priors

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I took this from wikipedia. If you check with what ever your likelihood and priors parameters are it probably all works out (you did not add these in the question)

From a quick google, here's a link to someone going through the proof: link

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