Symmetry and context

Topic: The Beta–Binomial model · more questions on this topic
‹ The pseudo-count trap A proper nonconjugate prior ›

Show that a prior density satisfying p(\theta)=p(1-\theta) has \mathbb{E}(\theta)=1/2 whenever the expectation exists. Explain why this symmetry may be defensible for a newly minted coin but not for a coin selected because it repeatedly behaved strangely.

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