Suppose that you have prior beliefs about an unknown quantity which can be approximated by an

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Suppose that you have prior beliefs about an unknown quantity θ which can be approximated by an N(λ,ϕ) distribution, while my beliefs can be approximated by an N(μ,ψ) distribution. Suppose further that the reasons that have led us to these conclusions do not overlap with one another. What distribution should represent our beliefs about θ when we take into account all the information available to both of us?

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