If a distribution D over a finite set {1,2,,V} assigns probability pi to element (number) i, then the entropy of the distribution is defined to be ipilogpi1. For the rest of the question, let V denote the number of words in the English dictionary, and pi the unigram probability of the ith word in the dictionary. Let the entropy ipilogpi1 represent the word entropy of English. By definition, if we look at a corpus of length T, where T, then we expect to find the word i occurring close to piT times. (Formally, this follows from the central limit theorem, but you can assume it to be true). Using the previous fact, show that the logarithm of the perplexity of a unigram language model on a large held-out corpus C is the word entropy of English