The role of a Scrum Master in a Daily Scrum is often misunderstood. Firstly, we often talk about a Daily Stand-up, rather than a Daily Scrum. And then, teams often regards their Scrum Master as a kind of a Project Manager.
It is important to remember what Daily Scrum is really about. Let's look at the Scrum Guide as it has all the answers:
"At it [Daily Scrum], the Development Team plans work for the next 24 hours. This optimizes team collaboration and performance by inspecting the work since the last Daily Scrum and forecasting upcoming Sprint work."
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Professional Scrum Master II