Interpreting Context-Dependent Mathematical Notation

In a discussion about the statistical properties of a model's output, a researcher writes the following: 'Let X be a random variable representing the token ID produced by the model. We are interested in calculating ⟨X⟩.' What does the notation ⟨X⟩ represent in this specific context?

Consider the following two statements from different mathematical domains:

1. In a paper on probabilistic models, a researcher states: 'The average value of the output is calculated as ⟨Y⟩.'
2. In a textbook on group theory, an author writes: 'The set of all integer powers of an element g forms a subgroup, denoted ⟨g⟩.'

Based on these two examples, what is the most critical conclusion one can draw about the notation ⟨...⟩?