Let XXX have the PDF f(x)=2xf(x) = 2xf(x)=2x for 0≤x≤10 \le x \le 10≤x≤1. Calculate the entropy H(X)=−E[lnf(X)]H(X) = -E[\ln f(X)]H(X)=−E[lnf(X)].
H(X)=12−ln2H(X) = \frac{1}{2} - \ln 2H(X)=21−ln2
H(X)=ln2−12H(X) = \ln 2 - \frac{1}{2}H(X)=ln2−21
H(X)=12+ln2H(X) = \frac{1}{2} + \ln 2H(X)=21+ln2
H(X)=14−ln2H(X) = \frac{1}{4} - \ln 2H(X)=41−ln2