 Binary entropy function

The binary entropy function isIt is concave on $[0,1]$ and satisfies $H_2(x)\ge 2x$ for $0\le x\le 1/2$ by comparison with the chord from $(0,0)$ to $(1/2,1)$.

The binary entropy function quantifies the uncertainty associated with a binary random variable, which can take on two possible outcomes (commonly denoted as 0 and 1). It is an important concept in information theory, providing a measure of the amount of information or the level of disorder in a binary system.