Solution
= Solution
<Entropy> is nonnegative. Gibbs' inequality also gives
$$
H(X_1,ldots,X_n)\leq\log_2|A^n|=n\log_2 27.
$$
Divide by $n$ and pass to the assumed <limit> to obtain
$$
0\leq H_E\leq\log_2 27.
$$
= Solution
<Entropy> is nonnegative. Gibbs' inequality also gives
$$
H(X_1,ldots,X_n)\leq\log_2|A^n|=n\log_2 27.
$$
Divide by $n$ and pass to the assumed <limit> to obtain
$$
0\leq H_E\leq\log_2 27.
$$