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Variation of St. Petersburg Paradox
I was discussing the the St. Petersburg paradox and the following question came up:
Suppose the game doesn't end within nine rounds, then the player directly receives $2^{10}$ dollars , while ...
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Is there a name for this probabilistic paradox?
Let $X\sim Exp(1)$ and $Y\sim Exp(\lambda)$, independent. Then,
\begin{align}
f_{X|Y=mX}(x) = \frac{f_{X,Y}(x,mx) }{\int f_{X,Y}(x,mx) \:dx }=\frac{f_X(x)f_Y(mx) }{\int f_X(x)f_Y(mx) \:dx } = \frac{e^{...