Is this sentence correct?
I am to win the competition.
With this sentence I want to say that I must win the competition.
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In a comment, John Lawler wrote:
Must refers to an obligation; be to refers to an expectation. The periphrastic modal for must is have to; the periphrastic modal be to is one of the ways to paraphrase will; mostly it means 'be scheduled/expected to', rather than 'be obligated to'. Forget about the question mark.
1a) I am to win the competition? or
1b) I am to win the competition.
Would be understood as a question asking if the person's fate is to be the victor or indicating anticipation of this before it happens.
In other words:
2a) Am I to understand that I will win the competition? or
2b) I will be selected as the winner of the competition.
To express intent to win (confidently, even smugly), you could say:
I will win the competition.
Note that this exact same sentence could mean the same things as 1b or 2b above, so context would determine whether it is inevitable or just your intent.