- Joined
- 2/16/12
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I pick a number n from 1 to 100. If you guess correctly, I pay you $n and zero otherwise. How much would you pay to play this game?
The books explains:
The solution is to pick k with probability proportional to 1/k. We therefore pick k with probability
(1) \(\frac{1}{k} (\sum\limits_{j=1}^{100} \frac{1}{j})^{-1}\)
Our expected payout is then
\((\sum\limits_{j=1}^{100} \frac{1}{j})^{-1}\)
Can someone explain how Joshi arrives at (1)?
The books explains:
The solution is to pick k with probability proportional to 1/k. We therefore pick k with probability
(1) \(\frac{1}{k} (\sum\limits_{j=1}^{100} \frac{1}{j})^{-1}\)
Our expected payout is then
\((\sum\limits_{j=1}^{100} \frac{1}{j})^{-1}\)
Can someone explain how Joshi arrives at (1)?