Suppose I have an English dictionary, that is a list of words in a file. I have to calculate the entropy of the first char.
I calculated the probability of each first char ($P_a, P_b, \dots, P_z$) in this way:
$$P_a = \dfrac {\# \text{words that start with 'a'}} {\# \text{tot words in dictionary}} .$$
How can I calculate $H(\text{first char})$? I think it's:
$$H(X) = - \sum _{i=a, \dots, z} P_i \log_2 P_i$$
but I'm not sure.
Thanks.