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Frank Einstein

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Misplaced Homework Thread

**TL;DR Summary:**I want to find a function with f'>0, f''<0 and takes the values 2, 2^2, 2^3, 2^4,..., 2^n

Hello everyone.

A professor explained the St. Petersburgh paradox in class and the concept of utility function U used to explain why someone won't play a betting game with an infinite expected value.

Then he talked about Kar Meyer's finding of a bounded utility function and still infinite payoff and told us to find a bounded function with the following properties:

f'>0, f''<0 and takes the values 2, 2^2, 2^3, 2^4, ..., 2^n

The values 2, 2^2, 2^3, 2^4, ..., 2^n have to be taken for x=1,2,3,4,..., n.

I have been thinking and reading about this but I have found no answer. I have even read Meyer's article and there he says that if the amount gained per bet is exp(2^n) then the expected value of the logarithm of the gain is infinite.

Thus, I think that either my professor has made a mistake or is trolling my class. However, before writing an email telling him that what he asks is impossible I would like to see if someone here agrees or disagrees with me.

Any answer is appreciated.

Best regards.