Im supposed to calculate the entropy of following language $L=\{x,y,z,w\}$
Symbols have following probability of occurrence:
$p(x)=\frac{1}{2},\quad p(y)=\frac{1}{4},\quad p(z)=p(w)=\frac{1}{8}$
,and they occur independently.
Formula given is $$\lim_{n\rightarrow \infty}\frac{H(L^n)}{n}$$ and regular entropy $H(x)=-\sum p(x_i)\log p(x_i)$
I just can't figure out $H(L^n)$. For single symbol its easy, but having strings length of $n$.. Thanks in advance.
Hint:
Use the statement "they occur independently" to arrive at $$H(L^n)=nH(L).$$