If XXX has a MGF MX(t)=11−2tM_X(t) = \frac{1}{1-2t}MX(t)=1−2t1 for t<1/2t < 1/2t<1/2, what is the entropy H(X)H(X)H(X) of the distribution?
Not defined because the entropy of continuous variables is not unique
1+ln(2)1 + \ln(2)1+ln(2)
ln(2)\ln(2)ln(2)
Depends on the variance