# Understanding variational inference for Bayesian GMM

I am reading Variational Inference: A Review for Statisticians by Blei, Kucukelbir and McAuliffe. I am having a hard time following some of the steps in Section 3.2

More precisely, they state that $$\phi_{ik}$$ = $$E[c_{ik};\phi_{i}$$]. I am not sure I follow this. I understand that $$c_{i}$$ is an indicator vector and that $$q(c_{i};\phi_{i})$$ is the distribution on the mixture assignment of the $$i$$th observation vector. The statement in that particular statement goes onto say that because $$c_{i}$$ is an indicator vector, this follows. I am not sure I follow it.

Would appreciate an explanation of this.