## Sampling-Drugs

Suppose one has a bunch of drugs $d_1, \dots , d_n$ that have similar effects (e.g. they all treat the flu). But suppose that $d_t$ where $t \in \{1, \dots , n \}$ has the highest response rate. In other words, $d_t$ is chosen to be the drug that combats the flu (even though all the others do as well). Is it the case that $d_t$ will always mask the effects of the rest of the drugs? How does $I/H$ respond in this situation? Note that $I$ is the mutual information and $H$ is the joint entropy. In other words, we are considering

$\frac{I(X,Y)}{H(X,Y)} = \frac{\sum_{x,y} p(x,y) \log \frac{p(x,y)}{p(x)p(y)}}{\sum_{x,y} p(x,y) \log p(x,y)}$