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A dealer's hit rate

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The chance that a dealer trades on your quote has a $Beta (3, 5)$ prior. You then send $12$ quotes and $9$ of them trade. What is the posterior mean of that chance? Give a fraction.

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Hint

Add trades to the first parameter and misses to the second.

Solution

The posterior is $Beta (3 + 9, 5 + 3) = Beta (12, 8)$ .
Its mean is $\frac{12}{12 + 8} = \frac{3}{5}$ .

Answer: $\frac{3}{5}$

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