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3176概率困难derivationmedium

Aggressive vs Defensive Quote After a Signal

题目

There are two possible actions. Aggressive pays 10 in the good state and -8 in the bad state. Defensive pays 4 in the good state and -1 in the bad state. The good state has prior probability 25\frac{2}{5}. Before acting, you may see a binary signal that is correct with probability 45\frac{4}{5}. What is the value of observing the signal, and which action should you take after a good signal and after a bad signal?

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你的答案

value of observing the signal

action without signal

action after good signal

action after bad signal