Representing a word by its co-occurrences with other words in context is an effective way to capture the meaning of the word. However, the theory behind remains a challenge. In this work, taking the example of a word classification task, we give a theoretical analysis of the approaches that represent a word X by a function f(P(C|X)), where C is a context feature, P(C|X) is the conditional probability estimated from a text corpus, and the function f maps the co-occurrence measure to a prediction score. We investigate the impact of context feature C and the function f. We also explain the reasons why using the co-occurrences with multiple context features may be better than just using a single one. In addition, some of the results shed light on the theory of feature learning and machine learning in general.