You have a coin with probability of heads p, but p is unknown. Your prior for p is Uniform[0,1]. You flip it once and it lands heads. I want to buy a derivative that pays $1 if the next flip is also heads. As a market maker, what is your fair price?
你面前有一枚硬币，掷出正面的概率是 p，你完全不知道 p 是多少，所以假设它在 [0,1] 上均匀分布。你掷了一次发现是正面。现在我要买一个衍生品，如果下一次也是正面，它支付1块钱。作为做市商，你的公允报价是多少？