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A conditional entropy can be expressed in the following way, H_{V_t}(V_s) = -\sum_{s,t}p(s,t)\log{p_t(s)} = -\sum_{s,t}p(s,t)\log{\frac{p(s,t)}{\sum_{s'}{p(s',t)}}}

$s$ and $t$ are defined on finite domain, say $s,t\in{\{00,01,11,10\}}$. Each value of $p(s,t)$ is an independent variable. Is conditional entropy a convex function under this circumstances?

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    variable is $p(s,t)$, not $s$ and $t$. The question is also improved accordingly.2012-02-13

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