# what is the relationship between entropy and variance?

Consider a simple Bernoulli variable X

X = 1 with probability p
X = 0 with probability (1-p)


The variance is simply p(1-p). The entropy is -p*ln(p)-(1-p)*ln(1-p) Both are measures of uncertainty. What is the advantage of entropy then?

Thanks!

They measure different things. Given the variance, you can solve for $$p$$ and compute the entropy, and vice versa, but they have different interpretations and different applications. You can learn a bit about the meaning and applications of these notions in the corresponding Wikipedia articles: https://en.wikipedia.org/wiki/Entropy_(information_theory), https://en.wikipedia.org/wiki/Variance.