The annotations of explicit and implicit discourse connectives in the Penn Discourse Treebank make it possible to investigate on a large scale how different types of discourse relations are expressed. Assuming an account of the Uniform Information Density hypothesis, we expect that discourse relations should be expressed explicitly with a discourse connector when they are unexpected, but may be implicit when the discourse relation can be anticipated. We investigate whether discourse relations which have been argued to be expected by the comprehender exhibit a higher ratio of implicit connectors. We find support for two hypotheses put forth in previous research which suggest that continuous and causal relations are presupposed by language users when processing consecutive sentences in a text. We then proceed to analyze the effect of Implicit Causality (IC) verbs (which have been argued to raise an expectation for an explanation) as a local cue for an upcoming causal relation.