What is the entropy H(X)H(X)H(X) of a Bernoulli(p)\text{Bernoulli}(p)Bernoulli(p) variable?
−plnp−(1−p)ln(1−p)-p\ln p - (1-p)\ln(1-p)−plnp−(1−p)ln(1−p)
plnp+(1−p)ln(1−p)p\ln p + (1-p)\ln(1-p)plnp+(1−p)ln(1−p)
lnp+ln(1−p)\ln p + \ln(1-p)lnp+ln(1−p)
p(1−p)p(1-p)p(1−p)