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# -*- coding: utf-8 -*-
# <nbformat>3.0</nbformat>

# <headingcell level=1>

# "Chance to beat" or C2B empirical estimation

# <markdowncell>

# We define two and independent random variables $A$ and $B$ and their probability density, respectively $f_A :\mathbb{R} \mapsto [0;1]$ and $f_B: \mathbb{R} \mapsto [0;1]$. The "chance to beat" probability, or $C2B$, is the probability that a sample from $B$ is greater than a sample from $A$, i.e.

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