What is the entropy H(X)H(X)H(X) of a discrete random variable XXX with P(X=1)=pP(X=1) = pP(X=1)=p and P(X=0)=1−pP(X=0) = 1-pP(X=0)=1−p?
−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)